Hostname: page-component-7dd5485656-jtdwj Total loading time: 0 Render date: 2025-10-31T02:47:58.334Z Has data issue: false hasContentIssue false
  • English
  • Français

On certain subalgebras of a dual B*-algebra

Published online by Cambridge University Press:  09 April 2009

Pak-Ken Wong
Pak-Ken Wong
Affiliation:
Department of Mathematics Seton Hall University, South Orange, New Jersey 07079, U.S.A.
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.

Let A be a dual B*-algebra and Ap the p-class in A. We show that the conjugate space of A1 is A**, the second conjugate space of A. We also obtain a three lines theorem for Ap (1 ≦p≦∞).

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 1 , February 1977 , pp. 105 - 111
Copyright
Copyright © Australian Mathematical Society 1977

References

Gohberg, I. C. and Krein, M. G. (1969), ‘Introduction to the theory of linear nonselfadjoint operators in a Hilbert space’, (Transl. Math. Monographs. 18, Amer. Math. Soc. Providence, R. I., 1969).Google Scholar
McCarthy, C. A. (1967), ‘cp’, Israel J. Math. 5, 249–271.CrossRefGoogle Scholar
Rickart, C. E. (1960), ‘General theory of Banach algebras’, (University series in Higher Math., Van Nostrand, Princeton, N. J., 1960).Google Scholar
Sakai, S. (1971), ‘C*-algebras and W*-algebras’, (Ergebnisse der Math. und ihrer Grenzgebiete Heft 60, Springer-Verlag, Berlin, 1971).Google Scholar
Saworotnow, P. P. (1970), ‘Trace-class and centralizers of an H*-algebra’, Proc. Amer. Math. Soc. 26, 101–104.Google Scholar
Saworotnow, P. P. and Friedell, J. C. (1970), ‘Trace-class for an arbitary H*-algebra’, Proc. Amer. Soc. 26, 95–100.Google Scholar
Schatten, R. (1960), ‘Norm ideals of completely continuous operators’, (Ergebnisse der Math. und ihrer Grenzgebiete, Heft 27. Springer-Verlag, Berlin, 1960).Google Scholar
Wong, P. K. (1971), ‘On the Arens product and annihilator algebras’, Proc. Amer. Math. Soc. 30, 79–83.CrossRefGoogle Scholar
Wong, P. K. (1973), ‘On the Arens products and certain Banach algebras’, Trans. Amer. Math. Soc. 180, 437–448.CrossRefGoogle Scholar
Wong, P. K. (1974), ‘The p-class in a dual B*-algebra’, Trans. Amer. Math. Soc. 200, 355–368.Google Scholar