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Proceedings of the American Mathematical Society

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

 
 

 

Mapping properties of relatively regular operators


Author: S. R. Caradus
Journal: Proc. Amer. Math. Soc. 47 (1975), 409-412
DOI: https://doi.org/10.1090/S0002-9939-1975-0353022-9
MathSciNet review: 0353022
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Abstract | References | Additional Information

Abstract: A relatively regular operator is one with closed complemented range and nullspace. It is shown that if $ T$ is relatively regular and $ f$ is univalent on the spectrum of $ T$ with $ f(0) = 0$, then $ f(T)$ is also relatively regular.


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

  • [1] E. Asplund, A non-closed relative spectrum, Ark. Mat. 3 (1958), 425-427. MR 19, 968. MR 0091431 (19:968d)
  • [2] F. V. Atkinson, On relatively regular operators, Acta Sci. Math. (Szeged) 15 (1953), 38-56. MR 15, 134. MR 0056835 (15:134e)
  • [3] N. Dunford and J. T. Schwartz, Linear operators. I: General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958. MR 22 #8302. MR 0117523 (22:8302)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0353022-9
Keywords: Relatively regular operator, operational calculus
Article copyright: © Copyright 1975 American Mathematical Society

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