Hostname: page-component-77c89778f8-n9wrp Total loading time: 0 Render date: 2024-07-22T12:57:43.987Z Has data issue: false hasContentIssue false
  • English
  • Français

The quasi-strict topology on the space of quasi-multipliers of a B*-algebra

Published online by Cambridge University Press:  24 October 2008

M. S. Kassem  and
K. Rowlands
M. S. Kassem
Affiliation:
Department of Mathematics, Mansoura University, Egypt
K. Rowlands
Affiliation:
Department of Mathematics, University College of Wales, Aberystwyth
Get access Rights & Permissions [Opens in a new window]

Extract

The notion of a left (right, double) multiplier may be regarded as a generalization of the concept of a multiplier to a non-commutative Banach algebra. Each of these is a special case of a more general object, namely that of a quasi-multiplier. The idea of a quasi-multiplier was first introduced by Akemann and Pedersen in ([1], §4), where they consider the quasi-multipliers of a C*-algebra. One of the defects of quasi-multipliers is that, at least a priori, there does not appear to be a way of multiplying them together. The general theory of quasi-multipliers of a Banach algebra A with an approximate identity was developed by McKennon in [5], and in particular he showed that the quasi-multipliers of a considerable class of Banach algebras could be multiplied. McKennon also introduced a locally convex topology γ on the space QM(A) of quasi-multipliers of A and derived some of the elementary properties of (QM(A), γ).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 101 , Issue 3 , May 1987 , pp. 555 - 566
Copyright
Copyright © Cambridge Philosophical Society 1987

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Akemann, C. A. and Pedersen, G. K.. Complications of semicontinuity in C *-algebra theory. Duke Math. J. 40 (1973), 785–795.Google Scholar
[2]Busby, R. C.. Double centralizers and extensions of C *-algebras. Trans. Amer. Math. Soc. 132 (1968), 79–99.Google Scholar
[3]Heuser, H. G.. Functional Analysis (Wiley, 1982).Google Scholar
[4]Kaplansky, I.. The structure of certain operator algebras. Trans. Amer. Math. Soc. 70 (1951), 219–255.CrossRefGoogle Scholar
[5]McKennon, M.. Quasi-multipliers. Trans. Amer. Math. Soc. 233 (1977), 105–123.Google Scholar
[6]Taylor, D. C.. The strict topology for double centralizer algebras. Trans. Amer. Math. Soc. 150 (1970), 633–643.Google Scholar
[7]Tomiuk, B. J.. Multipliers on Banach algebras. Studia Math. 54 (1976), 267–283.CrossRefGoogle Scholar
[8]Tomiuk, B. J.. Arens regularity and the algebra of double multipliers. Proc. Amer. Math. Soc. 81 (1981), 293–298.Google Scholar
[9]Tomiuk, B. J. and Wong, P. K.. Arens product and duality in B *-algebras. Proc. Amer. Math. Soc. 25 (1970), 529–535.Google Scholar
[10]Vasudevan, R. and Goel, S.. Embedding of quasi-multipliers of a Banach algebra into its second dual. Math. Proc. Cambridge Philos. Soc. 95 (1984), 457–466.Google Scholar