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A NOTE ON POSITIVE ${\mathcal{A}}{\mathcal{N}}$ OPERATORS

Part of: General theory of linear operators Special classes of linear operators

Published online by Cambridge University Press:  26 December 2018

IAN DOUST Open the ORCID record for IAN DOUST [Opens in a new window]
IAN DOUST*
Affiliation:
School of Mathematics and Statistics, University of New South Wales, UNSW Sydney 2052, Australia email i.doust@unsw.edu.au
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Abstract

We show that positive absolutely norm attaining operators can be characterised by a simple property of their spectra. This result clarifies and simplifies a result of Ramesh. As an application we characterise weighted shift operators which are absolutely norm attaining.

Keywords

absolutely norm attaining operatorsweighted shift operators

MSC classification

Primary: 47A10: Spectrum, resolvent
Secondary: 47B10: Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 100 , Issue 1 , August 2019 , pp. 129 - 130
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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References

Carvajal, X. and Neves, W., ‘Operators that achieve the norm’, Integral Equations Operator Theory 72 (2012), 179–195.Google Scholar
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Pandey, S. K. and Paulsen, V. I., ‘A spectral characterization of AN operators’, J. Aust. Math. Soc. 102 (2017), 369–391.Google Scholar
Ramesh, G., ‘Absolutely norm attaining paranormal operators’, J. Math. Anal. Appl. 465 (2018), 547–556.Google Scholar