Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-15T18:34:58.128Z Has data issue: false hasContentIssue false
  • English
  • Français

The Measure Algebra as an Operator Algebra

Published online by Cambridge University Press:  20 November 2018

Donald E. Ramirez
Donald E. Ramirez*
Affiliation:
University of Virginia, Charlottesville, Virginia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In § I, it is shown that M(G)*, the space of bounded linear functionals on M(G), can be represented as a semigroup of bounded operators on M(G).

Let △ denote the non-zero multiplicative linear functionals on M(G) and let P be the norm closed linear span of △ in M(G)*. In § II, it is shown that P, with the Arens multiplication, is a commutative B*-algebra with identity. Thus P = C(B), where B is a compact, Hausdorff space.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1391 - 1396
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Arens, R., The adjoint of a bilinear operation, Proc. Amer. Math. Soc. 2 (1951), 839–848.Google Scholar
2. Birtel, F., On a commutative extension of a Banach algebra, Proc. Amer. Math. Soc. 13 (1962), 815–822.Google Scholar
3. Buck, R. C., Operator algebras and dual spaces, Proc. Amer. Math. Soc. 3 (1952), 681–687.Google Scholar
4. Civin, P. and Yood, B., The second conjugate space of a Banach algebra as an algebra, Pacific J. Math. 11 (1961), 847–870.Google Scholar
5. Eberlein, W., Characterizations of Fourier-Stieltjes transforms, Duke Math. J. 22 (1955), 465–468.Google Scholar
6. Hewitt, E. and Ross, K., Abstract harmonic analysis, Vol. I (Academic Press, New York, 1963).Google Scholar
7. Riefïel, M., Commutative group algebras and measure algebras, Trans. Amer. Math. Soc. 116 (1965), 32–65.Google Scholar
8. Stromberg, K., A note on the convolution of regular measures, Math. Scand. 7 (1959), 347–352.Google Scholar
9. Takeda, Z., Conjugate spaces of operator algebras, Proc. Japan Acad. 30 (1954), 90–95.Google Scholar
10. Taylor, J., The structure of convolution measure algebras, Trans. Amer. Math. Soc. 119 1965), 150–166.Google Scholar