Operators with a given part of the numerical range-Reference-Cited by-同舟云学术

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Operators with a given part of the numerical range

Published:2016-02-01 Issue:1 Volume:66 Page:275-280
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Bračič Janko¹,Diogo Cristina²

Affiliation:

1. University of Ljubljana IMFM, Jadranska ul. 19 SI–1000 Ljubljana SLOVENIA

2. Instituto Universitário de Lisboa (ISCTE-IUL) Avenida das Forças Armadas P–1649-026 Lisboa PORTUGAL and Center for Mathematical Analysis, Geometry, and Dynamical Systems Departamento de Matemática Instituto Superior Técnico P–1049-001 Lisboa PORTUGAL

Abstract

Abstract Sets of operators which have a given set of numbers in the numerical range are studied. We prove an interesting result which characterizes the set of operators that have 0 in the convex hull of its spectrum. Along the way we give a simpler proof of the well known Hilbebrandt’s theorem.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2015-0134/pdf

Reference8 articles.

1. Gustafson K. E.—Rao D. K. M.: Numerical Range, Springer-Verlag, New York, 1997.

2. Halmos P. R.: A Hilbert Space Problem Book, Springer-Verlag, New-York, 1982.

3. Hildebrandt S.: über den Numerischen Wertebereich eines Operators, Math. Ann. 163 (1966), 230–247.

4. Laursen K.B.—Neumann M.N.: An Introduction to Local Spectral Theory . London Math. Soc. Monogr. 20, Clarendon Press, Oxford, 2000.

5. Müller V.: Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras (2nd ed.). Oper. Theory Adv. Appl. 139, Birkhäuser, Basel, 2007.

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