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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Which operators are similar to partial isometries?
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by L. A. Fialkow PDF
Proc. Amer. Math. Soc. 56 (1976), 140-144 Request permission

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 $\mathcal {P} = \{ T{\text { in }}\mathcal {L}(\mathcal {H})|r(T) < 1{\text { and }}T{\text {is similar to a partial isometry with infinite rank} \}}$; let $\mathcal {S} = \{ S{\text { in }}\mathcal {L}(\mathcal {H})|r(S) < 1,{\text {range}}(S){\text { is closed, and rank}}(S)= {\text {nullity}}(S)= {\text {corank}}(S)={\aleph _0}\}$. 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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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 56 (1976), 140-144
  • MSC: Primary 47A65
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0412858-7
  • MathSciNet review: 0412858