Article
Mathematics, Applied
Ermin Wang, Jiajia Xu
Summary: This paper investigates the boundedness and compactness of Toeplitz operators between two large Fock spaces, which has significant implications in the fields of computer science and mathematics.
Article
Mathematics, Applied
Hong Rae Cho, Hyungwoon Koo, Young Joo Lee
Summary: In this study, we focus on the orthogonal complement of the polyanalytic Fock space to investigate the properties of dual Toeplitz operators. We characterize the zero sum of products of two dual Toeplitz operators with harmonic symbols. Our results extend several known results on the analytic Fock space to every polyanalytic Fock spaces.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Djordjije Vujadinovic
Summary: This article discusses the Schatten norm of nuclear operator B*αBα, and provides norm estimates for the Berezin transform in both Fock spaces and unweighted Lebesgue spaces.
Article
Mathematics
Kaikai Han, Maofa Wang, Qi Wu
Summary: This paper examines unbounded complex symmetric Toeplitz operators on the Hardy space and Fock space. The technique used to investigate their complex symmetry differs from that used for bounded Toeplitz operators.
ACTA MATHEMATICA SCIENTIA
(2022)
Article
Mathematics
Chunxu Xu, Tao Yu
Summary: We characterize the necessary and sufficient conditions for invertible Toeplitz operators acting on the Fock space. Specifically, we study the Fredholm properties of Toeplitz operators with BMO1 symbols, where their Berezin transforms are bounded functions of vanishing oscillation. By examining the winding of the Berezin transform along a sufficiently large circle, we show the Fredholm index of the Toeplitz operator and provide a characterization for invertible Toeplitz operators with non-negative symbols that may be unbounded, but have bounded and oscillation-vanishing Berezin transforms.
Article
Mathematics, Applied
Yufei Li
Summary: In this paper, the commutant of the truncated Toeplitz operator on K-theta(2) with symbol z(n) is characterized using the commutant lifting theorem. The study determines when A(zn)(theta) is multiplicity free, thereby extending previous results and solving a conjecture.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics
Zhangjian Hu, Jani A. Virtanen
Summary: This paper provides a complete characterization of Schatten class Hankel operators H-f acting on weighted Segal-Bargmann spaces F-2(phi) using the notion of integral distance to analytic functions in C-n and Hörmander's partial derivative-theory. Based on our characterization, for f ∈ L-infinity and 1 < p < infinity, we prove that H-f is in the Schatten class S-p if and only if H ((f) over bar) ∈ S-p,S-, which was previously known only for the Hilbert-Schmidt class S-2 of the standard Segal-Bargmann space F-2(phi) with phi(z) = alpha vertical bar z vertical bar(2).
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics
Zhamgjian Hu, Jani A. Virtanen
Summary: The authors present a valid proof of Theorem 1.2 and rectify the statement of Theorem 2.6 in their paper published in Trans. Amer. Math. Soc. 375 (2022), 3733-3753.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2023)
Article
Mathematics
Chunxu Xu, Tao Yu
Summary: The study explores the properties of the generalized Toeplitz operator T-mu((j)) on the unit disk with a finite positive measure mu, discussing conditions for boundedness and compactness. It provides necessary and sufficient conditions for the operator in the Schatten p-class on the Bergman space A(2), as well as sufficient conditions for the Schatten p-class (0<p<1) on A(2). Additionally, it examines generalized Toeplitz operators with general bounded symbols and characterizes the compactness of finite sums of operators in the form of T-phi 1((j)) . . . T-phi n((j)) on the Bergman space A(p) with phi in L-infinity(D, dA) and 1<p<infinity.
CZECHOSLOVAK MATHEMATICAL JOURNAL
(2021)
Article
Mathematics
Arup Chattopadhyay, Soma Das, Chandan Pradhan, Srijan Sarkar
Summary: This article introduces a new class of conjugations and provides characterization of complex symmetric Toeplitz operators. Moreover, a characterization of complex symmetric block Toeplitz operators is obtained.
LINEAR & MULTILINEAR ALGEBRA
(2023)
Article
Mathematics, Applied
Antonio Galbis
Summary: We obtain an estimate for the norm of selfadjoint Toeplitz operators with a radial, bounded and integrable symbol, highlighting that the norm of such operator is strictly less than the supremum norm of the symbol. Consequences for time-frequency localization operators are also discussed.
COMPLEX ANALYSIS AND OPERATOR THEORY
(2022)
Article
Mathematics, Applied
Gelu Popescu
Summary: The paper explores noncommutative m-hyperballs and their applications, including multi-Toeplitz operators with harmonic symbols, Cauchy duals, free semigroups, etc. By generalizing the model, it tackles problems related to multi-pluriharmonic functions with operator coefficients.
Article
Mathematics
Junta Du, Songxiao Li
Summary: This paper investigates Schatten-Herz class Toeplitz operators on weighted Bergman spaces induced by doubling weights.
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
(2021)
Article
Mathematics
Jingbo Xia
Summary: The paper proved an exact integral formula for the Schatten p-norm of Hankel operators on the one-variable Hardy space for p = 2, 4, and 6. It was also shown that these are the only values of p for which such a formula is possible. Furthermore, it was pointed out that the only meaningful multi-variable analogue of this formula is when n = 2 and p = 6.
JOURNAL OF FUNCTIONAL ANALYSIS
(2021)
Article
Mathematics, Applied
Yong Chen, Young Joo Lee, Yile Zhao
Summary: In this study, we examined truncated Toeplitz operators on infinite dimensional model spaces and their commutators with symbols induced by certain inner functions, describing their kernels and ranks. Our findings extend recent results by Chen et al. to infinite dimensional model spaces.
BANACH JOURNAL OF MATHEMATICAL ANALYSIS
(2021)
