Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ON THE RELATION BETWEEN COMPACTNESS AND STRUCTURE OF CERTAIN OPERATORS ON SPACES OF ANALYTIC FUNCTIONS

  • ROBATI, B. KHANI (Dept. of Mathematics, Shiraz University)
  • Received : 1999.11.22
  • Published : 2001.07.30
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Abstract

Let $\mathcal{B}$ be a Banach space of analytic functions defined on the open unit disk. Assume S is a bounded operator defined on $\mathcal{B}$ such that S is in the commutant of $M_zn$ or $SM_zn=-M_znS$ for some positive integer n. We give necessary and sufficient condition between compactness of $SM_z+cM_zS$ where c = 1, -1, i, -i, and the structure of S. Also we characterize the commutant of $M_zn$ for some positive integer n.

Keywords

Acknowledgement

Supported by : Shiraz University

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