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Proceedings of the American Mathematical Society

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



Operators satisfying certain growth conditions. II

Author: B. C. Gupta
Journal: Proc. Amer. Math. Soc. 58 (1976), 148-150
MSC: Primary 47A65
MathSciNet review: 0417831
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Abstract: It is proved that the condition $ {w_\rho }[{(T - zI)^{ - 1}}] = 1/d(z,\sigma (T)),{w_\rho }( \cdot )$ being the operator radius of Holbrook, implies the existence of certain eigenvalues and normal eigenvalues for a Hilbert space operator $ T$. This extends known results based on a norm condition $ (\rho = 1)$ and allows a similar extension of various consequences of these results.

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Keywords: $ \rho $-dilation, operator radius, isoloid operators, $ {M_\rho }$-operators
Article copyright: © Copyright 1976 American Mathematical Society

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