Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1976-0417831-0
MathSciNet review: 0417831
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A65

Retrieve articles in all journals with MSC: 47A65


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0417831-0
Keywords: $ \rho $-dilation, operator radius, isoloid operators, $ {M_\rho }$-operators
Article copyright: © Copyright 1976 American Mathematical Society