This is an announcement for the paper "Amenability of algebras of approximable operators" by Ariel Blanco and Niels Groenbaek.

Abstract: We give a necessary and sufficient condition for amenability of the Banach algebra of approximable operators on a Banach space. We further investigate the relationship between amenability of this algebra and factorization of operators, strengthening known results and developing new techniques to determine whether or not a given Banach space carries an amenable algebra of approximable operators. Using these techniques, we are able to show, among other things, the non-amenability of the algebra of approximable operators on Tsirelson's space.

Archive classification: math.FA

Mathematics Subject Classification: 46B20, 47L10 (primary), 16E40 (secondary)

Remarks: 20 pages, to appear in Israel Journal of Mathematics

The source file(s), OnAmenability2.tex: 82733 bytes, is(are) stored in gzipped form as 0804.1725.gz with size 25kb. The corresponding postcript file has gzipped size 148kb.

Submitted from: gronbaek@math.ku.dk

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http://front.math.ucdavis.edu/0804.1725

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http://arXiv.org/abs/0804.1725

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