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- W2080266767 abstract "In this paper, we study the closed subalgebra AT of ℬ(ℋ) generated by an operator T. We show that AT is amenable if and only if T is similar to a normal operator whose spectrum has connected complement and no interior. Furthermore, if AT is amenable, then AT is similar to a C*-algebra. We also prove that if T has finite spectrum, then AT is weakly amenable if and only if AT is amenable. In particular, if Q ∈ ℬ(ℋ) is quasinilpotent, then AQ is weakly amenable if and only if Q = 0." @default.
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- W2080266767 date "2005-05-01" @default.
- W2080266767 modified "2023-10-17" @default.
- W2080266767 title "Amenable operators on Hilbert spaces" @default.
- W2080266767 doi "https://doi.org/10.1515/crll.2005.2005.582.201" @default.
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