This is an announcement for the paper "Compact multipliers on spaces of analytic functions" by Pawel Mleczko.
Abstract: In the paper compact multiplier operators on Banach spaces of analytic functions on the unit disk with the range in Banach sequence lattices are studied. If the domain space $X$ is such that $H_\infty\hookrightarrow X\hookrightarrow H_1$, necessary and sufficient conditions for compactness are presented. Moreover, the calculation of the Hausdorff measure of noncompactness for diagonal operators between Banach sequence lattices is applied to obtaining the characterization of compact multipliers in case the domain space $X$ satisfies $H_\infty\hookrightarrow X\hookrightarrow H_2$.
Archive classification: math.FA math.CV
Mathematics Subject Classification: 42B15, 42B30, 46E05, 7B10
The source file(s), comp-multi.tex: 26131 bytes, is(are) stored in gzipped form as 0808.1359.gz with size 9kb. The corresponding postcript file has gzipped size 82kb.
Submitted from: pml@amu.edu.pl
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http://arXiv.org/abs/0808.1359
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