Multiplier operators on 𝐵*-algebras

Malviya, B. D.; Tomiuk, B. J.

doi:10.1090/S0002-9939-1972-0305085-1

Multiplier operators on $B^{\ast }$-algebras
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by B. D. Malviya and B. J. Tomiuk

Proc. Amer. Math. Soc. 31 (1972), 505-510

DOI: https://doi.org/10.1090/S0002-9939-1972-0305085-1

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Abstract:

The purpose of this paper is to give a characterization of the dual ${B^\ast }$-algebra and the algebra of bounded linear operators on Hilbert space in terms of their multipliers.

References

Richard Arens, The adjoint of a bilinear operation, Proc. Amer. Math. Soc. 2 (1951), 839–848. MR 45941, DOI 10.1090/S0002-9939-1951-0045941-1
F. F. Bonsall and A. W. Goldie, Annihilator algebras, Proc. London Math. Soc. (3) 4 (1954), 154–167. MR 61768, DOI 10.1112/plms/s3-4.1.154
Paul Civin and Bertram Yood, The second conjugate space of a Banach algebra as an algebra, Pacific J. Math. 11 (1961), 847–870. MR 143056, DOI 10.2140/pjm.1961.11.847
Irving Kaplansky, The structure of certain operator algebras, Trans. Amer. Math. Soc. 70 (1951), 219–255. MR 42066, DOI 10.1090/S0002-9947-1951-0042066-0
L. Máté, Embedding multiplier operators of a Banach algebra $B$ into its second conjugate space $B^{\ast \ast }$, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 13 (1965), 809–812 (English, with Russian summary). MR 192362
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
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, DOI 10.1007/978-3-642-87652-3
B. J. Tomiuk and Pak-ken Wong, The Arens product and duality in $B^{\ast }$-algebras, Proc. Amer. Math. Soc. 25 (1970), 529–535. MR 259620, DOI 10.1090/S0002-9939-1970-0259620-0
Kenneth G. Wolfson, The algebra of bounded operators on Hilbert space, Duke Math. J. 20 (1953), 533–538. MR 60160