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

Published online by Cambridge University Press:  08 July 2016

SATISH K. PANDEY
Affiliation:
Department of Pure Mathematics, University of Waterloo, Ontario, Canada N2L 3G1 email satish.pandey@uwaterloo.ca
VERN I. PAULSEN
Affiliation:
Department of Pure Mathematics, University of Waterloo, Ontario, Canada N2L 3G1 email vpaulsen@uwaterloo.ca
Corresponding
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Abstract

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.

Type
Research Article
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), 179195.CrossRefGoogle Scholar
Halmos, P., A Hilbert Space Problem Book (Springer, New York, 1982).CrossRefGoogle 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), 386395.CrossRefGoogle Scholar
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