Left centralizers of an -algebra
Authors:
Gregory F. Bachelis and James W. McCoy
Journal:
Proc. Amer. Math. Soc. 43 (1974), 106-110
MSC:
Primary 46K15
DOI:
https://doi.org/10.1090/S0002-9939-1974-0333745-7
MathSciNet review:
0333745
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Abstract | References | Similar Articles | Additional Information
Abstract: An explicit characterization is given of the left centralizers of a proper -algebra
. Each left centralizer is seen to correspond to a bounded family of bounded operators, where each operator acts on a Hilbert space associated with a minimal-closed two-sided ideal of
.
- [1] Wai-mee Ching and James S. W. Wong, Multipliers and 𝐻* algebras, Pacific J. Math. 22 (1967), 387–395. MR 215106
- [2] Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups, Die Grundlehren der mathematischen Wissenschaften, Band 152, Springer-Verlag, New York-Berlin, 1970. MR 0262773
- [3] B. E. Johnson, An introduction to the theory of centralizers, Proc. London Math. Soc. (3) 14 (1964), 299–320. MR 0159233, https://doi.org/10.1112/plms/s3-14.2.299
- [4] B. E. Johnson and A. M. Sinclair, Continuity of derivations and a problem of Kaplansky, Amer. J. Math. 90 (1968), 1067–1073. MR 239419, https://doi.org/10.2307/2373290
- [5] Irving Kaplansky, Dual rings, Ann. of Math. (2) 49 (1948), 689–701. MR 25452, https://doi.org/10.2307/1969052
- [6] C. N. Kellogg, Centralizers and 𝐻*-algebras, Pacific J. Math. 17 (1966), 121–129. MR 193529
- [7] B. D. Malviya and B. J. Tomiuk, Multiplier operators on 𝐵*-algebras, Proc. Amer. Math. Soc. 31 (1972), 505–510. MR 305085, https://doi.org/10.1090/S0002-9939-1972-0305085-1
- [8] Charles E. Rickart, General theory of Banach algebras, The University Series in Higher Mathematics, D. van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0115101
- [9] Parfeny P. Saworotnow, Trace-class and centralizers of an 𝐻*-algebra, Proc. Amer. Math. Soc. 26 (1970), 101–104. MR 267403, https://doi.org/10.1090/S0002-9939-1970-0267403-0
- [10] Parfeny P. Saworotnow and John C. Friedell, Trace-class for an arbitrary 𝐻*-algebra, Proc. Amer. Math. Soc. 26 (1970), 95–100. MR 267402, https://doi.org/10.1090/S0002-9939-1970-0267402-9
- [11] Robert Schatten, Norm ideals of completely continuous operators, Ergebnisse der Mathematik und ihrer Grenzgebiete. N. F., Heft 27, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960. MR 0119112
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1974-0333745-7
Article copyright:
© Copyright 1974
American Mathematical Society