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Proceedings of the American Mathematical Society

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Operators with left inverses similar to their adjoints


Author: S. M. Patel
Journal: Proc. Amer. Math. Soc. 41 (1973), 127-131
MSC: Primary 47A65
DOI: https://doi.org/10.1090/S0002-9939-1973-0322558-7
MathSciNet review: 0322558
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Abstract: The primary object of this paper is to show that if $ T$ is a left invertible operator with a left inverse $ {T_1}$ and if there exists an operator $ S$ such that $ {T^ \ast } = {S^{ - 1}}{T_1}S$ and $ 0 \notin {\text{cl}}(W(S))$, then $ T$ is similar to an isometry.


References [Enhancements On Off] (What's this?)

  • [1] V. Istrăţescu and I. Istrătescu, On some classes of operators. II, Math. Ann. 194 (1971), 126-134. MR 44 #7351. MR 0290166 (44:7351)
  • [2] C. R. Putnam, The spectra of operators having resolvent of first order growth, Trans. Amer. Math. Soc. 133 (1968), 505-510. MR 37 #4651. MR 0229073 (37:4651)
  • [3] U. N. Singh and Kanta Mangla, Operators with inverses similar to their adjoints, Proc. Amer. Math. Soc. 38 (1973), 258-260. MR 0310688 (46:9786)
  • [4] J. P. Williams, Operators similar to their adjoints, Proc. Amer. Math. Soc. 20 (1969), 121-123. MR 38 #1552. MR 0233230 (38:1552)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0322558-7
Keywords: Left inverse, cramped operator, normaloid, polar decomposition, numerical range, left essential spectrum
Article copyright: © Copyright 1973 American Mathematical Society

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