Boundedness and compactness of operators on the Fock space
Xiaofeng Wang, Guangfu Cao, and Kehe Zhu
TL;DR
This paper establishes conditions under which operators on the Fock space are bounded or compact, and characterizes compactness via the Berezin transform.
Contribution
It provides new sufficient conditions for boundedness and compactness of operators on the Fock space, including a characterization using the Berezin transform.
Findings
Sufficient conditions for operator boundedness on Fock space
Characterization of compactness via Berezin transform
Conditions linking boundedness and compactness
Abstract
We obtain sufficient conditions for a densely defined operator on the Fock space to be bounded or compact. Under the boundedness condition we then characterize the compactness of the operator in terms of its Berezin transform.
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Taxonomy
TopicsHolomorphic and Operator Theory · Mathematical Analysis and Transform Methods · Spectral Theory in Mathematical Physics