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2018 On the algebra of WCE operators
Yousef Estaremi
Rocky Mountain J. Math. 48(2): 501-517 (2018). DOI: 10.1216/RMJ-2018-48-2-501

Abstract

In this paper, we consider the algebra of WCE operators on $L^p$-spaces, and we investigate some al\-ge\-braic properties of it. For instance, we show that the set of normal WCE operators is a unital finite Von Neumann algebra, and we obtain the spectral measure of a normal WCE operator on $L^2(\mathcal {F})$. Then, we specify the form of projections in the Von Neumann algebra of normal WCE operators, and we obtain that, if the underlying measure space is purely atomic, then all projections are minimal. In the non-atomic case, there is no minimal projection. Also, we give a non-commutative operator algebra on which the spectral map is subadditive and submultiplicative. As a consequence, we obtain that the set of quasinilpotents is an ideal, and we get a relation between quasinilpotents and commutators. Moreover, we give some sufficient conditions for an algebra of WCE operators to be triangularizable, and consequently, that its quotient space over its quasinilpotents is commutative.

Citation

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Yousef Estaremi. "On the algebra of WCE operators." Rocky Mountain J. Math. 48 (2) 501 - 517, 2018. https://doi.org/10.1216/RMJ-2018-48-2-501

Information

Published: 2018
First available in Project Euclid: 4 June 2018

zbMATH: 06883478
MathSciNet: MR3809155
Digital Object Identifier: 10.1216/RMJ-2018-48-2-501

Subjects:
Primary: 47L80

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 2 • 2018
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