Absolutely norm attaining paranormal operators

G, Ramesh (2018) Absolutely norm attaining paranormal operators. Journal of Mathematical Analysis and Applications, 465 (1). pp. 547-556. ISSN 0022-247X

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Abstract

A bounded linear operator , where are Hilbert spaces is said to be norm attaining if there exists a unit vector such that . If for any closed subspace M of , the restriction of T to M is norm attaining, then T is called an absolutely norm attaining operator or -operator. We prove the following characterization theorem: a positive operator T defined on an infinite dimensional Hilbert space H is an -operator if and only if the essential spectrum of T is a single point and contains atmost finitely many points. Here and are the minimum modulus and essential minimum modulus of T, respectively. As a consequence we obtain a sufficient condition under which the -property of an operator implies -property of its adjoint. We also study the structure of paranormal -operators and give a necessary and sufficient condition under which a paranormal -operator is normal.

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IITH Creators:
IITH CreatorsORCiD
G, RameshUNSPECIFIED
Item Type: Article
Uncontrolled Keywords: Compact operator, Norm attaining operator, Weyl's theorem, Paranormal operator, Reducing subspace
Subjects: Mathematics
Divisions: Department of Mathematics
Depositing User: Team Library
Date Deposited: 12 Jul 2018 06:58
Last Modified: 12 Jul 2018 06:58
URI: http://raiith.iith.ac.in/id/eprint/4240
Publisher URL: http://doi.org/10.1016/j.jmaa.2018.05.024
OA policy: http://www.sherpa.ac.uk/romeo/issn/0022-247X/
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