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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Operators satisfying certain growth conditions
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by S. M. Patel and B. C. Gupta
Proc. Amer. Math. Soc. 53 (1975), 341-346
DOI: https://doi.org/10.1090/S0002-9939-1975-0385617-0

Abstract:

Let $T$ be an operator on a complex Hilbert space $H$. Some growth conditions on operator radius of the resolvent of $T$ are studied. Moreover, it is shown that the conjecture, due to V. Istrătescu, that for operators $T$ satisfying growth condition $({{\text {G}}_1})$ \[ \sup \limits _{||x|| = 1} \;\{ ||Tx|{|^2} - |(Tx,\;x){|^2}\} = R_T^2,\] where ${R_T}$ is the radius of the smallest circular disk containing the spectrum $\sigma (T)$, turns out to be false.
References
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Bibliographic Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 53 (1975), 341-346
  • MSC: Primary 47A65
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0385617-0
  • MathSciNet review: 0385617