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arXiv · 1404.3405

Finie dimensional invariant subspace property and amenability for a class of Banach algebras

Anthony T. -M. Lau·Yong Zhang
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Abstract

Motivated by a result of Ky Fan in 1965, we establish a characterization of a left amenable F-algebra (which includes the group algebra and the Fourier algebra of a locally compact group and quantum group algebras, or more generally the predual algebra of a Hopf von Neumann algebra) in terms of a finite dimensional invariant subspace property. This is done by first revealing a fixed point property for the semigroup of norm one positive linear func- tionals in the algebra. Our result answers an open question posted in Tokyo in 1993 by the first author (see [25, Problem 5]). We also show that the left amenability of an ideal in an F-algebra may determine the left amenability of the algebra.

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Anthony T. -M. Lau, Yong Zhang. 2014-04-13. Finie dimensional invariant subspace property and amenability for a class of Banach algebras. https://arxiv.org/abs/1404.3405

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