Article
Mathematics
Xiaomin Wei, Lining Jiang, Dianlu Tian
Summary: This paper focuses on the crossed product A proportional to H, arising from the action of a finite Hopf C*-algebra on a C*-algebra of finite dimension. It constructs a linear functional on the *-algebra A proportional to H through a faithful positive Haar measure, showing it to be a faithful positive linear functional. The complete positivity of the positive linear functional is crucial in the argument, ultimately concluding that the crossed product A proportional to H is a C*-algebra of finite dimension under a faithful *- representation.
Article
Mathematics
Dan Ursu
Summary: The study provides complete descriptions of the tracial states on both the universal and reduced crossed products of a C*-dynamical system, answering questions about canonical bijections with invariant tracial states. Simplifications are made in various cases, while contradictory results are obtained in the case of abelian groups, including a finite-dimensional counterexample and a correction to a previous result.
ADVANCES IN MATHEMATICS
(2021)
Article
Multidisciplinary Sciences
Elif Igde, Koray Yilmaz
Summary: The study explores the relationship between Lie algebras and symmetric monoidal categories, which has significant applications in algebraic topology, representation theory, and quantum physics. The paper presents analogous definitions for Lie algebras using whiskered structures, bimorphisms, crossed complexes, crossed differential graded algebras, and tensor products. These definitions establish a direct correspondence between these algebraic structures and Lie algebras. The study also demonstrates that the 2-truncation of the crossed differential graded Lie algebra gives rise to a braided crossed module of Lie algebras, and constructs a functor to simplicial Lie algebras.
Article
Mathematics
Chafiq Benhida, Raill E. Curto, Sang Hoon Lee, Jasang Yoon
Summary: In this article, we investigate the spectral structure of the generalized spherical Aluthge transform Delta(t)(T) of a d-tuple T of Hilbert space operators, and prove that the spectral radius of T can be calculated from the norms of the iterates of Delta(t)(T). We also provide an example where the formula fails for d = t = 1.
ADVANCES IN MATHEMATICS
(2022)
Article
Mathematics
Tattwamasi Amrutam, Dan Ursu
Summary: We prove a generalized version of Powers' averaging property and apply it to generalize results of Hartman and Kalantar as well as Kawabe. Furthermore, we generalize a result of the first named author and Kalantar on simplicity of intermediate C*-algebras.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics, Applied
Sana Bouzidi, Nedra Moalla, Ines Walha
Summary: In this paper, we introduce a newly proposed perturbation concept called Phi-perturbation function originated by M. Mbekhta in 2004. We use this concept to derive original stability results in the theory of perturbed Fredholm operators. Furthermore, we investigate a new characterization of the Weyl spectrum of linear operators under the Phi-perturbation function. Finally, we study the stability of perturbed semi-Fredholm operators using this function approach, and provide illustrative examples.
COMPLEX ANALYSIS AND OPERATOR THEORY
(2022)
Article
Mathematics, Applied
Quan-guo Chen
Summary: This paper presents a new approach for constructing weak crossed products.
Article
Mathematics
Chi-Keung Ng, ZhaoLin Yao
Summary: The text discusses properties of group actions on algebras, specifically focusing on the strong property T. It shows conditions where the property T of the group and algebra can affect the property T of the crossed product. The results are based on existing research and generalizations of previous findings.
LINEAR & MULTILINEAR ALGEBRA
(2021)
Article
Mathematics
Arkady Kitover, Mehmet Orhon
Summary: The paper investigates properties of essential spectra of disjointness preserving operators acting on Banach C(K)-modules. It proves that under certain conditions, the upper semi-Fredholm spectrum of such operators is rotation invariant. The paper also provides a full description of the spectrum and essential spectra of operators acting on Kaplansky modules of a specific form.
Article
Mathematics
Camila F. Sehnem
Summary: This article investigates the C*-algebra structure of product systems and submonoids of groups, proving several isomorphisms between different C*-algebras and answering an open question. The results of this study are important for understanding the applications of these algebraic structures in mathematics.
JOURNAL OF FUNCTIONAL ANALYSIS
(2022)
Article
Mathematics, Applied
Slim Chelly
Summary: This paper introduces the notion of relative demicompact elements of an algebra with respect to a Banach subalgebra, which is a generalization of relative demicompact linear operators in Banach spaces. Based on this concept, a new class of Fredholm perturbation is constructed for a given Banach subalgebra B, which includes its inessential ideal kB and the set of left Fredholm perturbations. This class of Fredholm perturbation reveals that it is a two-sided closed ideal in B, playing a crucial role in characterizing the weyl spectrum of elements affiliated with B.
Article
Mathematics, Applied
Hamadi Baklouti, Sirine Namouri
Summary: This paper introduces the invertibility of positive bounded operators in Hilbert spaces and discusses spectral analysis in relation to this concept. This new notion is of significant importance for studies in non-Hermitian quantum mechanics.
BANACH JOURNAL OF MATHEMATICAL ANALYSIS
(2022)
Article
Mathematics
Hatem Baloudi
Summary: Muraleetharan and Thirulogasanthar (J. Math. Phys. 2018;59(10):103506, 27p.) introduced the concept of the Calkin S-spectrum of a bounded quaternionic linear operator and studied it using Fredholm operator theory. They also investigated the general framework of the Fredholm element with respect to a quaternionic Banach algebra homomorphism, explored the properties of the Fredholm S-spectrum and proved a perturbation result on this spectrum. Additionally, they studied the boundary S-spectrum and applied it to the study of the Fredholm and Weyl S-spectra of bounded right quaternionic linear operators.
LINEAR & MULTILINEAR ALGEBRA
(2023)
Article
Mathematics, Applied
Jacopo Bassi
Summary: Introduced an analogue of orbit-breaking subalgebra for free flows on locally compact metric spaces, which has an approximate structure with a fixed point and nested sequence of central slices. It is shown that for minimal flows with a compact Cantor central slice, the resulting C*-algebra is the stabilization of Putnam's orbit-breaking subalgebra associated with the induced homeomorphism on the central slice. This construction provides an alternative characterization (up to stabilization) of Putnam's orbit-breaking subalgebra for minimal homeomorphisms of Cantor spaces in terms of suspension flows associated with such dynamical systems.
RESULTS IN MATHEMATICS
(2023)
Article
Mathematics, Applied
Eusebio Gardella, Ilan Hirshberg, Luis Santiago
Summary: This study examines compact group actions with finite Rokhlin dimension, focusing on their relationship with crossed products. By characterizing the duals of such actions and determining the ideal structure of their crossed products, the study extends previous results on the Rokhlin property. It is shown that under certain assumptions, taking crossed products by these actions preserves various classes of C*-algebras, including those with D-absorbing properties, stability, and specific nuclear, stable, and K-theory properties. These results are new and significant even in the well-studied case of the Rokhlin property. Additionally, the study demonstrates that finite Rokhlin dimension with commuting towers implies the (weak) tracial Rokhlin property, with core arguments based on local approximations of crossed products by continuous C(X)-algebras.
ERGODIC THEORY AND DYNAMICAL SYSTEMS
(2021)
Article
Mathematics, Applied
Vladimir Georgescu, Christian Gerard, Dietrich Haefner
JOURNAL OF SPECTRAL THEORY
(2015)
Article
Physics, Multidisciplinary
Vladimir Georgescu, Manuel Larenas, Avy Soffer
ANNALES HENRI POINCARE
(2016)
Article
Mathematics
Vladimir Georgescu, Victor Nistor
JOURNAL OF OPERATOR THEORY
(2017)
Article
Mathematics, Applied
V. Georgescu, C. Gerard, D. Hafner
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
(2017)
Article
Physics, Multidisciplinary
Laurent Bruneau, Jan Derezinski, Vladimir Georgescu
ANNALES HENRI POINCARE
(2011)
Article
Mathematics
Vladimir Georgescu, Victor Nistor
COMPTES RENDUS MATHEMATIQUE
(2014)
Article
Mathematics
Mondher Damak, Vladimir Georgescu
JOURNAL OF FUNCTIONAL ANALYSIS
(2010)
Article
Mathematics
Vladimir Georgescu
JOURNAL OF FUNCTIONAL ANALYSIS
(2011)
Article
Mathematics
V. Georgescu, C. Gerard, D. Haefner
JOURNAL OF FUNCTIONAL ANALYSIS
(2013)
Article
Mathematics
E. B. Davies, V. Georgescu
JOURNAL OF OPERATOR THEORY
(2013)
Article
Physics, Multidisciplinary
Jan Derezinski, Vladimir Georgescu
ANNALES HENRI POINCARE
(2020)
Review
Physics, Mathematical
Vladimir Georgescu, Andrei Iftimovici
REVIEWS IN MATHEMATICAL PHYSICS
(2006)
Article
Mathematics
V. Georgescu, S. Golenia
JOURNAL OF OPERATOR THEORY
(2008)
Article
Mathematics
Vladimir Georgescu
JOURNAL OF FUNCTIONAL ANALYSIS
(2007)
Article
Mathematics, Applied
Geunsu Choi, Mingu Jung, Sun Kwang Kim, Miguel Martin
Summary: This paper studies weak-star quasi norm attaining operators and proves that the set of such operators is dense in the space of bounded linear operators regardless of the choice of Banach spaces. It is also shown that weak-star quasi norm attaining operators have distinct properties from other types of norm attaining operators, although they may share some equivalent properties under certain conditions.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maria Lorente, Francisco J. Martin-Reyes, Israel P. Rivera-Rios
Summary: In this paper, we provide quantitative one-sided estimates that recover the dependences in the classical setting. We estimate the one-sided maximal function in Lorentz spaces and demonstrate the applicability of the conjugation method for commutators in this context.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Fernando Cobos, Luz M. Fernandez-Cabrera
Summary: We provide a necessary and sufficient condition for the weak compactness of bilinear operators interpolated using the real method. However, this characterization does not hold for interpolated operators using the complex method.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ovgue Gurel Yilmaz, Sofiya Ostrovska, Mehmet Turan
Summary: The Lupas q-analogue Rn,q, the first q-version of the Bernstein polynomials, was originally proposed by A. Lupas in 1987 but gained popularity 20 years later when q-analogues of classical operators in approximation theory became a focus of intensive research. This work investigates the continuity of operators Rn,q with respect to the parameter q in both the strong operator topology and the uniform operator topology, considering both fixed and infinite n.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
M. Agranovsky, A. Koldobsky, D. Ryabogin, V. Yaskin
Summary: This article modifies the concept of polynomial integrability for even dimensions and proves that ellipsoids are the only convex infinitely smooth bodies satisfying this property.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Abel Komalovics, Lajos Molnar
Summary: In this paper, a parametric family of two-variable maps on positive cones of C*-algebras is defined and studied from various perspectives. The square roots of the values of these maps under a faithful tracial positive linear functional are considered as a family of potential distance measures. The study explores the problem of well-definedness and whether these distance measures are true metrics, and also provides some related trace characterizations. Several difficult open questions are formulated.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Frederic Bayart
Summary: The passage describes the construction of an operator on a separable Hilbert space that is 5-hypercyclic for all δ in the range (ε, 1) and is not 5-hypercyclic for all δ in the range (0, ε).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Helene Frankowska, Nikolai P. Osmolovskii
Summary: This paper investigates second-order optimality conditions for the minimization problem of a C2 function f on a general set K in a Banach space X. Both necessary and sufficient conditions are discussed, with the sufficiency condition requiring additional assumptions. The paper demonstrates the validity of these assumptions for the case when the set K is an intersection of sets described by smooth inequalities and equalities, such as in mathematical programming problems. The novelty of the approach lies in the arbitrary nature of the set K and the straightforward proofs.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ole Fredrik Brevig, Kristian Seip
Summary: This paper studies the Hankel operator on the Hardy space and discusses its minimal and maximal norms, as well as the relationship between the maximal norm and the properties of the function.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Alexander Meskhi
Summary: Rubio de Francia's extrapolation theorem is established for new weighted grand Morrey spaces Mp),lambda,theta w (X) with weights w beyond the Muckenhoupt Ap classes. This result implies the one-weight inequality for operators of Harmonic Analysis in these spaces for appropriate weights. The necessary conditions for the boundedness of the Hardy-Littlewood maximal operator and the Hilbert transform in these spaces are also obtained. Some structural properties of new weighted grand Morrey spaces are investigated. Problems are studied in the case when operators and spaces are defined on spaces of homogeneous type.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maud Szusterman
Summary: In this work, the necessary conditions on the structure of the boundary of a convex body K to satisfy all inequalities are investigated. A new solution for the 3-dimensional case is obtained in particular.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Rami Ayoush, Michal Wojciechowski
Summary: In this article, lower bounds for the lower Hausdorff dimension of finite measures are provided under certain restrictions on their quaternionic spherical harmonics expansions. This estimate is analogous to a result previously obtained by the authors for complex spheres.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
F. G. Abdullayev, V. V. Savchuk
Summary: This paper investigates the convergence and theorem proof of the Takenaka-Malmquist system and Fejer-type operator on the unit circle, and provides relevant results on the class of holomorphic functions representable by Cauchy-type integrals with bounded densities.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Sofiya Ostrovska, Mikhail I. Ostrovskii
Summary: This work aims to establish new results on the structure of transportation cost spaces. The main outcome of this paper states that if a metric space X contains an isometric copy of L1 in its transportation cost space, then it also contains a 1-complemented isometric copy of $1.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Pilar Rueda, Enrique A. Sanchez Perez
Summary: We prove a factorization theorem for Lipschitz operators acting on certain subsets of metric spaces of measurable functions and with values on general metric spaces. Our results show how a Lipschitz operator can be extended to a subset of other metric space of measurable functions that satisfies the following optimality condition: it is the biggest metric space, formed by measurable functions, to which the operator can be extended preserving the Lipschitz constant. Also, we demonstrate the coarsest metric that can be given for a metric space in which an order bounded lattice-valued-Lipschitz map is defined, and provide concrete examples involving the relevant space L0(mu).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)