Compact Operators via the Berezin Transform

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dc.creatorAxler, Sheldon
dc.creatorZheng, Dechao
dc.date1998-07-27
dc.date.accessioned2026-07-07T05:25:31Z
dc.date.available2026-07-07T05:25:31Z
dc.descriptionIn this paper we prove that if S equals a finite sum of finite products of Toeplitz operators on the Bergman space of the unit disk, then S is compact if and only if the Berezin transform of S equals 0 on the boundary of the disk. This result is new even when S equals a single Toeplitz operator. Our main result can be used to prove, via a unified approach, several previously known results about compact Toeplitz operators, compact Hankel operators, and appropriate products of these operators.
dc.description15 pages. To appear in Indiana University Mathematics Journal. For more information, see http://math.sfsu.edu/axler/CompactBerezin.html
dc.identifierhttps://arxiv.org/abs/math/9807147
dc.identifierhttp://arxiv.org/abs/math/9807147
dc.identifierIndiana Univ. Math. J. 47 (1998), 387-400
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77209
dc.subjectFunctional Analysis
dc.subject47B35, 46E20
dc.titleCompact Operators via the Berezin Transform
dc.typetext

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