Moving Weyl’s Theorem from f (T ) to T

doi:10.17398/2605-5686.33.2.209

Autores/as

  • M. Febronio Rodríguez BUAP, Facultad de Ciencias Fı́sico-Matemáticas Río Verde y Av. San Claudio, San Manuel, Puebla, Pue. 72570, Mexico
  • B.P. Duggal 8 Redwood Grove, Northfield Avenue, London W5 4SZ, England, U.K.
  • S.V. Djordjević BUAP, Facultad de Ciencias Fı́sico-Matemáticas Río Verde y Av. San Claudio, San Manuel, Puebla, Pue. 72570, Mexico

Palabras clave:

Weyl’s theorem, Browder’s theorem, SVEP

Resumen

Schmoeger has shown that if Weyl’s theorem holds for an isoloid Banach space operator TB(X) with stable index, then it holds for f (T ) whenever f ∈ Holo σ(T ) is a function holomorphic on some neighbourhood of the spectrum of T . In this note we establish a converse.

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Referencias

P. Aiena, “ Fredholm and Local Spectral Theory, with Applications to Multipliers ”, Kluwer Academic Publishers, Dordrecht, 2004.

B.P. Duggal, Hereditarily polaroid operators, SVEP and Weyl’s theorems, J. Math. Anal. Appl. 340 (2008), 366 – 373.

B.P. Duggal, Polaroid operators satisfying Weyl’s theorem, Linear Algebra Appl. 414 (2006), 271 – 277.

B.P. Duggal, SVEP, Browder and Weyl theorems, in “ Topics in Approximation Theory III ”, Dirección de Fomento Editorial BUAP, Puebla, Mexico, 2009, 107 – 146.

K.B. Laursen, M.M. Neumann, “ An Introduction to Local Spectral Theory ”, The Clarendon Press, Oxford University Press, New York, 2000.

R. Harte, On local spectral theory, in “ Recent Advances in Operator Theory and Applications ”, Birkhäuser, Basel, 2009, 175 – 183.

M. Oudghiri, Weyl’s and Browder’s theorems for operators satisfying the SVEP, Studia Math. 163 (2004), 85 – 101.

C. Schmoeger, On operators T such that Weyl’s theorem holds for f (T ), Extracta Math. 13 (1998), 27 – 33.

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Publicado

2018-12-01

Número

Sección

Operator Theory

Cómo citar

Moving Weyl’s Theorem from f (T ) to T: doi:10.17398/2605-5686.33.2.209. (2018). Extracta Mathematicae, 33(2), 209-218. https://revista-em.unex.es/index.php/EM/article/view/2605-5686.33.2.209