Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Multipliers on dual $ A\sp*$-algebras


Author: B. J. Tomiuk
Journal: Proc. Amer. Math. Soc. 62 (1977), 259-265
MSC: Primary 46K99; Secondary 46M05
MathSciNet review: 0433215
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let A be an $ {A^\ast}$-algebra which is a dense $ ^\ast$-ideal of a $ {B^\ast}$-algebra $ \mathfrak{A}$. We use tensor products and the algebra $ {M_l}(A)$ of left multipliers on A to obtain a characterization of duality in A. We show, moreover, that if A is dual then $ {M_l}(A)$ is algebra isomorphic to the second conjugate space $ {\mathfrak{A}^{\ast \ast}}$ of $ \mathfrak{A}$ when $ {\mathfrak{A}^{\ast \ast}}$ is given Arens product.


References [Enhancements On Off] (What's this?)

  • [1] B. A. Barnes, Subalgebras of modular annihilator algebras, Proc. Cambridge Philos. Soc. 66 (1969), 5-12. MR 41 #4236. MR 0259599 (41:4236)
  • [2] B. D. Malviya and B. J. Tomiuk, Multiplier operators on $ {B^\ast}$-algebras, Proc. Amer. Math. Soc. 31 (1972), 505-510. MR 46 #4215. MR 0305085 (46:4215)
  • [3] L. Máté, On representation of module-homomorphisms (multipliers), Studia Sci. Math. Hungar. 8 (1973), 187-192. MR 51 #1286. MR 0365033 (51:1286)
  • [4] T. Ogasawara and K. Yoshinaga, Weakly completely continuous $ Banac{h^\ast}$-algebras, J. Sci. Hiroshima Univ. Ser. A 18 (1954), 15-36. MR 16, 1126. MR 0070068 (16:1126d)
  • [5] C. E. Rickart, General theory of Banach algebras, Van Nostrand, Princeton, N.J., 1960. MR 22 #5903. MR 0115101 (22:5903)
  • [6] M. Rieffel, Induced Banach representations of Banach algebras and locally compact groups, J. Functional Analysis 1 (1967), 443-491. MR 36 #6544. MR 0223496 (36:6544)
  • [7] H. H. Schaefer, Topological vector spaces, Macmillan, New York, 1966. MR 33 #1689. MR 0193469 (33:1689)
  • [8] B. J. Tomiuk, Multipliers and duality in $ {A^\ast}$-algebras, Proc. Amer. Math. Soc. 50 (1975), 281-288. MR 51 #8834. MR 0372627 (51:8834)
  • [9] Pak-ken Wong, Modular annihilator $ {A^\ast}$-algebras, Pacific J. Math. 37 (1971), 825-834. MR 46 #4231. MR 0305083 (46:4213)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46K99, 46M05

Retrieve articles in all journals with MSC: 46K99, 46M05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0433215-4
PII: S 0002-9939(1977)0433215-4
Keywords: Dual $ {A^\ast}$-algebra, multipliers, Arens product, projective tensor product, Banach A-module
Article copyright: © Copyright 1977 American Mathematical Society