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arXiv · 1008.5238

Invariant and hyperinvariant subspaces for amenable operators

Luo Yi Shi·Yu Jing Wu·You Qing Ji
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Abstract

There has been a long-standing conjecture in Banach algebra that every amenable operator is similar to a normal operator. In this paper, we study the structure of amenable operators on Hilbert spaces. At first, we show that the conjecture is equivalent to every non-scalar amenable operator has a non-trivial hyperinvariant subspace and equivalent to every amenable operator is similar to a reducible operator and has a non-trivial invariant subspace; and then, we give two decompositions for amenable operators, which supporting the conjecture.

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Luo Yi Shi, Yu Jing Wu, You Qing Ji. 2010-08-31. Invariant and hyperinvariant subspaces for amenable operators. https://arxiv.org/abs/1008.5238

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