Geodesic
Isomorphisms of multiplier algebras
Glasgow mathematical journal, Tome 28 (1986) no. 1, pp. 73-77

Voir la notice de l'article provenant de la source Cambridge University Press

Let A and B be semisimple Banach algebras, and let M1(A) (resp. M1(B)) be the algebra of left multipliers on A (resp. B). Suppose that A is an abstract Segal algebra in B. We find conditions on A and B which imply that M1(A) is topologically algebra isomorphic to M1(B). As a special case we obtain the result of [8] which states that if A is an A*-algebra that is a*-ideal in its B*-algebra completion B and A2 is dense in A then M1(A) is topologically algebra isomorphic to M1(B). We make an application of our main result to right complemented Banach algebras. 
Tomiuk, B. J. Isomorphisms of multiplier algebras. Glasgow mathematical journal, Tome 28 (1986) no. 1, pp. 73-77. doi: 10.1017/S0017089500006364
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[1] 1.Alexander, F. E., On complemented and annhilator algebras, Proc. Glasgow Math. Assoc. 10 (1969), 38–45. Google Scholar | DOI

[2] 2.Bachelis, G. F., Homomorphisms of annihilator Banach algebras, Pacific J. Math. 25 (1968), 229–247. Google Scholar | DOI

[3] 3.Barnes, B. A., Banach algebras which are ideals in a Banach algebra, Pacific J. Math. 38 (1971) 1–7. Google Scholar | DOI

[4] 4.Cleveland, S. B., Homomorphisms of non-commutative *-algebras, Pacific J. Math. 13 (1963), 1097–1109. Google Scholar | DOI

[5] 5.Dixmier, J., Les C*-algèbres et leurs représentations (Gauthier-Villers, 1969). Google Scholar

[6] 6.Hewitt, E. and Ross, K. A., Abstract harmonic analysis II (Springer-Verlag, 1970). Google Scholar

[7] 7.Johnson, B. E. and Sinclair, A. M., Continuity of derivations and a problem of Kaplansky, Amer. J. Math. 90 (1968), 1067–1073. Google Scholar | DOI

[8] 8.Johnson, D. L. and Lahr, C. D., Multipliers of A*-algebras, Proc. Amer. Math. Soc. 74 (1979), 311–314. Google Scholar

[9] 9.Leinert, M., A contribution to Segal algebras, Manuscripta Math. 10 (1973), 297–306. Google Scholar | DOI

[10] 10.Malviya, B. D. and Tomiuk, B. J., Multiplier operators on B*-algebras, Proc. Amer. Math. Soc. 31 (1972), 505–510. Google Scholar

[11] 11.Tomiuk, B. J., Structure theory of complemented Banach algebras, Canad. J. Math. 14 (1962), 651–659. Google Scholar | DOI

[12] 12.Tomiuk, B. J. and Yood, B., Topological algebras with dense socle, J. Funct. Anal. 28 (1978), 254–277. Google Scholar | DOI

[13] 13.Tomiuk, B. J. and Yood, B., Incomplete normed algebras norms on Banach algebras, submitted. Google Scholar

[14] 14.Yood, B., One-sided ideals in Banach algebras, J. Nigerian Math. Soc., 1 (1982), 25–30. Google Scholar

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