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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, CanadaN2L 3G1 email [email protected]
VERN I. PAULSEN
Affiliation:
Department of Pure Mathematics, University of Waterloo, Ontario, CanadaN2L 3G1 email [email protected]
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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.

Type
Research Article
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

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