Toeplitz algebras over Fock and Bergman spaces
Shengkun Wu, Xianfeng Zhao

TL;DR
This paper investigates Toeplitz algebras on p-Fock and p-Bergman spaces, showing they are generated by Toeplitz operators with symbols in certain translation invariant subalgebras of bounded uniformly continuous functions, extending previous results.
Contribution
It demonstrates that Toeplitz algebras on these spaces are linearly generated by Toeplitz operators with symbols in specific subalgebras, answering open questions and generalizing known results.
Findings
Toeplitz algebra on p-Fock space generated by translation invariant symbols
Toeplitz algebra on p-Bergman space equals the linear span of Toeplitz operators with such symbols
Generalizes previous results for p=2 to all 1<p<∞
Abstract
In this paper, we study Toeplitz algebras generated by certain class of Toeplitz operators on the -Fock space and the -Bergman space with . Let BUC() and BUC() denote the collections of bounded uniformly continuous functions on and (the unit ball in ), respectively. On the -Fock space, we show that the Toeplitz algebra which has a translation invariant closed subalgebra of BUC() as its set of symbols is linearly generated by Toeplitz operators with the same space of symbols. This answers a question recently posed by Fulsche \cite{Robert}. On the -Bergman space, we study Toeplitz algebras with symbols in some translation invariant closed subalgebras of BUC(. In particular, we obtain that the Toeplitz algebra generated by all Toeplitz operators with symbols in BUC($\mathbb…
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Taxonomy
TopicsHolomorphic and Operator Theory · Algebraic and Geometric Analysis · Advanced Topics in Algebra
