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arXiv:math/9807147 [math.FA]AbstractReferencesReviewsResources

Compact Operators via the Berezin Transform

Sheldon Axler, Dechao Zheng

Published 1998-07-27Version 1

In 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.

Comments: 15 pages. To appear in Indiana University Mathematics Journal. For more information, see http://math.sfsu.edu/axler/CompactBerezin.html
Journal: Indiana Univ. Math. J. 47 (1998), 387-400
Categories: math.FA
Subjects: 47B35, 46E20
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