Commutators on a separable $L^{p}$-space
HTML articles powered by AMS MathViewer
- by Charles Schneeberger PDF
- Proc. Amer. Math. Soc. 28 (1971), 464-472 Request permission
Abstract:
A commutator is a bounded operator which can be expressed as a difference ABβBA 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.References
- F. Bohnenblust, An axiomatic characterization of $L_p$-spaces, Duke Math. J. 6 (1940), 627β640. MR 2701, DOI 10.1215/S0012-7094-40-00648-2
- Arlen Brown, P. R. Halmos, and Carl Pearcy, Commutators of operators on Hilbert space, Canadian J. Math. 17 (1965), 695β708. MR 203460, DOI 10.4153/CJM-1965-070-7
- Arlen Brown and Carl Pearcy, Structure of commutators of operators, Ann. of Math. (2) 82 (1965), 112β127. MR 178354, DOI 10.2307/1970564
- Paul R. Halmos, Commutators of operators. II, Amer. J. Math. 76 (1954), 191β198. MR 59484, DOI 10.2307/2372409
- P. R. Halmos, A glimpse into Hilbert space, Lectures on Modern Mathematics, Vol. I, Wiley, New York, 1963, pp.Β 1β22. MR 0178330 K. Shoda, Einige SΓ€tze ΓΌber Matrizen, Japan J. Math. 17 (1936), 361-365.
Additional Information
- © Copyright 1971 American Mathematical Society
- 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