In this paper, we study band-dominated operators on Bergman-type spaces and prove that the $C^*$-algebra of band-dominated operators is equal to the essential commutant of Toeplitz operators with a symbol in the set of bounded vanishing Lipschitz functions. On the Bergman space and the Fock space, we show that the $C^*$-algebra of band-dominated operators equals the Toeplitz algebra.
Shengkun Wu
,
Dechao Zhen
. BAND-DOMINATED OPERATORS ON BERGMAN-TYPE SPACES*[J]. Acta mathematica scientia, Series B, 2023
, 43(1)
: 387
-408
.
DOI: 10.1007/s10473-023-0122-7
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