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D. R. Farenick, B. E. Forrest, L. W. Marcoux

Amenable operators on Hilbert spaces

In this paper, we study the closed subalgebra A_T of ?(?) generated by an operator T. We show that A_T is amenable if and only if T is similar to a normal operator whose spectrum has connected complement and no interior. Furthermore, if A_T is amenable, then A_T is similar to a C*-algebra. We also prove that if T has finite spectrum, then A_T is weakly amenable if and only if A_T is amenable. In particular, if Q ? ?(?) is quasinilpotent, then A_Q is weakly amenable if and only if Q = 0.

Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter

Print ISSN: 0075-4102
Volume: 2005, 05/2005
Pages: 201 - 228

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