Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Duality in $ B\sp{\ast} $-algebras


Author: Sheila A. McKilligan
Journal: Proc. Amer. Math. Soc. 38 (1973), 86-88
MSC: Primary 46J10; Secondary 46K05
DOI: https://doi.org/10.1090/S0002-9939-1973-0326396-0
MathSciNet review: 0326396
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ X$ be a locally compact Hausdorff space and let $ {C_0}(X)$ be the algebra of continuous functions on $ X$ vanishing at infinity. Then $ {C_0}(X)$ is a dual algebra if and only if the operator $ \mu \to fd\mu $ is weakly completely continuous on $ {C_0}{(X)^ \ast }$ for all $ f \in {C_0}(X)$. This improves a recent result of P. K. Wong and provides a description of dual $ {B^ \ast }$-algebras.


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

  • [1] P. Civin and B. Yood, The second conjugate space of a Banach algebra as an algebra, Pacific J. Math. 11 (1961), 847-870. MR 26 #622. MR 0143056 (26:622)
  • [2] N. Dunford and J. T. Schwartz, Linear operators. I: General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958. MR 22 #8302. MR 0117523 (22:8302)
  • [3] E. Hewitt and K. A. Ross, Abstract harmonic analysis. Vol. I: Structure of topological groups. Integration theory, group representations, Die Grundlehren der math. Wissenschaften, Band 115, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 28 #158. MR 551496 (81k:43001)
  • [4] B. J. Tomiuk and P. K. Wong, The Arens product and duality in $ {B^ \ast }$-algebras, Proc. Amer. Math. Soc. 25 (1970), 529-535. MR 41 #4256. MR 0259620 (41:4256)
  • [5] P. K. Wong, The Arens product and duality in $ {B^ \ast }$-algebras. II, Proc. Amer. Math. Soc. 27 (1971), 535-538. MR 43 #933. MR 0275176 (43:933)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46J10, 46K05

Retrieve articles in all journals with MSC: 46J10, 46K05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0326396-0
Keywords: Dual $ {B^ \ast }$-algebra, weakly completely continuous operators
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society