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A Spectral Characterization of $\mathcal{AN}$ Operators (1501.05869v2)
Published 23 Jan 2015 in math.FA
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.
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