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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Which operators are similar to partial isometries?


Author: L. A. Fialkow
Journal: Proc. Amer. Math. Soc. 56 (1976), 140-144
MSC: Primary 47A65
MathSciNet review: 0412858
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Abstract: Let $ \mathcal{H}$ denote a separable, infinite dimensional complex Hilbert space and let $ \mathcal{L}(\mathcal{H})$ denote the algebra of all bounded linear operators on $ \mathcal{H}$. Let $ \mathcal{P} = \{ T{\text{ in }}\mathcal{L}(\mathcal{H})\vert r(T) < 1{\text{ and }}T{\text{is similar to a partial isometry with infinite rank} \}}$; let $ \mathcal{S} = \{ S{\text{ in }}\mathcal{L}(\mathcal{H})\vert r(S) < 1,{\text{r... ...s closed, and rank}}(S)= {\text{nullity}}(S)= {\text{corank}}(S)={\aleph _0}\} $. It is conjectured that $ \mathcal{P} = \mathcal{S}$ and it is proved that $ \mathcal{P} \subset \mathcal{S} \subset {\mathcal{P}^ - }$.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0412858-7
Article copyright: © Copyright 1976 American Mathematical Society