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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
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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

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References

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