The generalized Toeplitz operators on the Fock space F α 2

Chunxu Xu; Tao Yu

Czechoslovak Mathematical Journal (2024)

  • Issue: 1, page 231-246
  • ISSN: 0011-4642

Abstract

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Let μ be a positive Borel measure on the complex plane ℂ n and let j = ( j 1 , ⋯ , j n ) with j i ∈ ℕ . We study the generalized Toeplitz operators T μ ( j ) on the Fock space F α 2 . We prove that T μ ( j ) is bounded (or compact) on F α 2 if and only if μ is a Fock-Carleson measure (or vanishing Fock-Carleson measure). Furthermore, we give a necessary and sufficient condition for T μ ( j ) to be in the Schatten p -class for 1 ≤ p < ∞ .

How to cite

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Xu, Chunxu, and Yu, Tao. "The generalized Toeplitz operators on the Fock space $F_{\alpha }^{2}$." Czechoslovak Mathematical Journal (2024): 231-246. <http://eudml.org/doc/299232>.

@article{Xu2024,
abstract = {Let $\mu $ be a positive Borel measure on the complex plane $\mathbb \{C\}^n$ and let $j=(j_1,\cdots ,j_n)$ with $j_i\in \mathbb \{N\}$. We study the generalized Toeplitz operators $T_\{\mu \}^\{(j)\}$ on the Fock space $F_\{\alpha \}^\{2\}$. We prove that $T_\{\mu \}^\{(j)\}$ is bounded (or compact) on $F_\{\alpha \}^\{2\}$ if and only if $\mu $ is a Fock-Carleson measure (or vanishing Fock-Carleson measure). Furthermore, we give a necessary and sufficient condition for $T_\{\mu \}^\{(j)\}$ to be in the Schatten $p$-class for $1\le p<\infty $.},
author = {Xu, Chunxu, Yu, Tao},
journal = {Czechoslovak Mathematical Journal},
keywords = {generalized Toeplitz operator; boundedness; compactness; Schatten class; Fock space},
language = {eng},
number = {1},
pages = {231-246},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The generalized Toeplitz operators on the Fock space $F_\{\alpha \}^\{2\}$},
url = {http://eudml.org/doc/299232},
year = {2024},
}

TY - JOUR
AU - Xu, Chunxu
AU - Yu, Tao
TI - The generalized Toeplitz operators on the Fock space $F_{\alpha }^{2}$
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 231
EP - 246
AB - Let $\mu $ be a positive Borel measure on the complex plane $\mathbb {C}^n$ and let $j=(j_1,\cdots ,j_n)$ with $j_i\in \mathbb {N}$. We study the generalized Toeplitz operators $T_{\mu }^{(j)}$ on the Fock space $F_{\alpha }^{2}$. We prove that $T_{\mu }^{(j)}$ is bounded (or compact) on $F_{\alpha }^{2}$ if and only if $\mu $ is a Fock-Carleson measure (or vanishing Fock-Carleson measure). Furthermore, we give a necessary and sufficient condition for $T_{\mu }^{(j)}$ to be in the Schatten $p$-class for $1\le p<\infty $.
LA - eng
KW - generalized Toeplitz operator; boundedness; compactness; Schatten class; Fock space
UR - http://eudml.org/doc/299232
ER -

References

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