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STRUCTURE THEOREM FOR $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathcal{AN}$-OPERATORS

Part of: General theory of linear operators

Published online by Cambridge University Press:  30 April 2014

G. RAMESH
G. RAMESH*
Affiliation:
Department of Mathematics, Indian Institute of Technology Hyderabad, Ordnance Factory Estate, Yeddumailaram 502 205, Andhra Pradesh, India email rameshg@iith.ac.in
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Abstract

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In this paper we prove a structure theorem for the class of $\mathcal{AN}$-operators between separable, complex Hilbert spaces which is similar to that of the singular value decomposition of a compact operator. Apart from this, we show that a bounded operator is $\mathcal{AN}$ if and only if it is either compact or a sum of a compact operator and scalar multiple of an isometry satisfying some condition. We obtain characterizations of these operators as a consequence of this structure theorem and deduce several properties which are similar to those of compact operators.

Keywords

-operatorcompact operatorisometryminimum modulus

MSC classification

Secondary: 47A75: Eigenvalue problems 47A10: Spectrum, resolvent
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 96 , Issue 3 , June 2014 , pp. 386 - 395
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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