Left centralizers of an 𝐻*-algebra

Bachelis, Gregory F.; McCoy, James W.

doi:10.1090/S0002-9939-1974-0333745-7

Left centralizers of an $H^{\ast }$-algebra
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by Gregory F. Bachelis and James W. McCoy PDF

Proc. Amer. Math. Soc. 43 (1974), 106-110 Request permission

Abstract:

An explicit characterization is given of the left centralizers of a proper ${H^\ast }$-algebra $A$. 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 $A$.

References

Wai-mee Ching and James S. W. Wong, Multipliers and $H^{\ast }$ algebras, Pacific J. Math. 22 (1967), 387–395. MR 215106
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
B. E. Johnson, An introduction to the theory of centralizers, Proc. London Math. Soc. (3) 14 (1964), 299–320. MR 159233, DOI 10.1112/plms/s3-14.2.299
B. E. Johnson and A. M. Sinclair, Continuity of derivations and a problem of Kaplansky, Amer. J. Math. 90 (1968), 1067–1073. MR 239419, DOI 10.2307/2373290
Irving Kaplansky, Dual rings, Ann. of Math. (2) 49 (1948), 689–701. MR 25452, DOI 10.2307/1969052
C. N. Kellogg, Centralizers and $H^{\ast }$-algebras, Pacific J. Math. 17 (1966), 121–129. MR 193529
B. D. Malviya and B. J. Tomiuk, Multiplier operators on $B^{\ast }$-algebras, Proc. Amer. Math. Soc. 31 (1972), 505–510. MR 305085, DOI 10.1090/S0002-9939-1972-0305085-1
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
Parfeny P. Saworotnow, Trace-class and centralizers of an $H^{\ast }$-algebra, Proc. Amer. Math. Soc. 26 (1970), 101–104. MR 267403, DOI 10.1090/S0002-9939-1970-0267403-0
Parfeny P. Saworotnow and John C. Friedell, Trace-class for an arbitrary $H^{\ast }$-algebra, Proc. Amer. Math. Soc. 26 (1970), 95–100. MR 267402, DOI 10.1090/S0002-9939-1970-0267402-9
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