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A SPECTRAL CHARACTERIZATION OF ${\mathcal{A}}{\mathcal{N}}$ OPERATORS

Part of: Linear spaces and algebras of operators Special classes of linear operators General theory of linear operators

Published online by Cambridge University Press:  08 July 2016

SATISH K. PANDEY  and
VERN I. PAULSEN
SATISH K. PANDEY*
Affiliation:
Department of Pure Mathematics, University of Waterloo, Ontario, CanadaN2L 3G1 email satish.pandey@uwaterloo.ca
VERN I. PAULSEN
Affiliation:
Department of Pure Mathematics, University of Waterloo, Ontario, CanadaN2L 3G1 email vpaulsen@uwaterloo.ca
*
✉satish.pandey@uwaterloo.ca
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Abstract

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We establish a spectral characterization theorem for the operators on complex Hilbert spaces of arbitrary dimensions that attain their norm on every closed subspace. The class of these operators is not closed under addition. Nevertheless, we prove that the intersection of these operators with the positive operators forms a proper cone in the real Banach space of hermitian operators.

Keywords

N operatorAN operator

MSC classification

Primary: 47B07: Operators defined by compactness properties
Secondary: 47A10: Spectrum, resolvent 47A75: Eigenvalue problems 47L25: Operator spaces (= matricially normed spaces) 47L05: Linear spaces of operators 47L07: Convex sets and cones of operators 47B65: Positive operators and order-bounded operators
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 102 , Issue 3 , June 2017 , pp. 369 - 391
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

Carvajal, X. and Neves, W., ‘Operators that achieve the norm’, Integral Equations Operator Theory 72(2) (2012), 179–195.CrossRefGoogle Scholar
Halmos, P., A Hilbert Space Problem Book (Springer, New York, 1982).Google Scholar
Kadison, R. V. and Ringrose, J. R., ‘Fundamentals of the theory of operator algebras’, in: Special Topics Volume III: Elementary theory—An Exercise Approach (Birkhäuser, Cambridge, MA, 1991).Google Scholar
Ramesh, G., ‘Structure theorem for -operators’, J. Aust. Math. Soc. 96(3) (2014), 386–395.CrossRefGoogle Scholar