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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Commutators on a separable $ L\sp{p}$-space


Author: Charles Schneeberger
Journal: Proc. Amer. Math. Soc. 28 (1971), 464-472
MSC: Primary 47.40
DOI: https://doi.org/10.1090/S0002-9939-1971-0285927-8
MathSciNet review: 0285927
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Abstract: A commutator is a bounded operator which can be expressed as a difference AB--BA using bounded operators $ A$ and $ B$. This paper investigates the problem of classifying an operator on a separable $ {L^p}$-space as either a commutator or a noncommutator. If $ 1 < p < \infty $, we show that compact operators are commutators and that a large class of multiplication operators consists of commutators.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0285927-8
Keywords: Commutators of operators, operators on Banach spaces, separable $ {L^p}$-spaces, operators as commutators, matricial commutators, compact operators, multiplication operators, spectral limit point
Article copyright: © Copyright 1971 American Mathematical Society