Details
| Original language | English |
|---|---|
| Article number | 108661 |
| Journal | Journal of functional analysis |
| Volume | 279 |
| Issue number | 7 |
| Early online date | 1 Jun 2020 |
| Publication status | Published - 15 Oct 2020 |
Abstract
We prove several results concerning the theory of Toeplitz algebras over p-Fock spaces using a correspondence theory of translation invariant symbol and operator spaces. The most notable results are: The full Toeplitz algebra is the norm closure of all Toeplitz operators with bounded uniformly continuous symbols. This generalizes a result obtained by J. Xia [25] in the case p=2, which was proven by different methods. Further, we prove that every Toeplitz algebra which has a translation invariant C⁎ subalgebra of the bounded uniformly continuous functions as its set of symbols is linearly generated by Toeplitz operators with the same space of symbols.
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In: Journal of functional analysis, Vol. 279, No. 7, 108661, 15.10.2020.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Correspondence theory on p-Fock spaces with applications to Toeplitz algebras
AU - Fulsche, Robert
N1 - Publisher Copyright: © 2020 Elsevier Inc.
PY - 2020/10/15
Y1 - 2020/10/15
N2 - We prove several results concerning the theory of Toeplitz algebras over p-Fock spaces using a correspondence theory of translation invariant symbol and operator spaces. The most notable results are: The full Toeplitz algebra is the norm closure of all Toeplitz operators with bounded uniformly continuous symbols. This generalizes a result obtained by J. Xia [25] in the case p=2, which was proven by different methods. Further, we prove that every Toeplitz algebra which has a translation invariant C⁎ subalgebra of the bounded uniformly continuous functions as its set of symbols is linearly generated by Toeplitz operators with the same space of symbols.
AB - We prove several results concerning the theory of Toeplitz algebras over p-Fock spaces using a correspondence theory of translation invariant symbol and operator spaces. The most notable results are: The full Toeplitz algebra is the norm closure of all Toeplitz operators with bounded uniformly continuous symbols. This generalizes a result obtained by J. Xia [25] in the case p=2, which was proven by different methods. Further, we prove that every Toeplitz algebra which has a translation invariant C⁎ subalgebra of the bounded uniformly continuous functions as its set of symbols is linearly generated by Toeplitz operators with the same space of symbols.
KW - Fock spaces
KW - Toeplitz algebras
U2 - 10.48550/arXiv.1911.12668
DO - 10.48550/arXiv.1911.12668
M3 - Article
AN - SCOPUS:85085743482
VL - 279
JO - Journal of functional analysis
JF - Journal of functional analysis
SN - 0022-1236
IS - 7
M1 - 108661
ER -