On the multiplier algebra of certain locally m-convex algebras

Document Type

Presentation Abstract

Presentation Date

4-17-2013

Abstract

If A is a topological algebra, a bounded mapping T : A → A is called a left (right) multiplier on E if T(xy) = T(x)y (resp. T(xy) = xT(y)) for all x; y ∈ A; it is called a two-sided multiplier on E if it is both a left and a right multiplier. Denote by ℳl(A), ℳr(A) and ℳ(A) the sets of all left, right and two-sided multipliers of A, respectively. Multipliers play an important role in different areas of mathematics with an algebra structure, due to important applications of non-normed topological algebras in other fields. In this talk, we describe the multiplier algebra of a certain locally m-convex algebra with involution and a perfect projective system of decomposition. We give conditions under which ℳ(A) is isomorphic to the inverse limit of the multiplier algebras of its normed factors; this happens, for instance, in locally m-convex H*-algebras. Moreover, we describe the multiplier algebra of a locally m-convex algebra under certain conditions. Suitable examples will be given.

Additional Details

Presented jointly with the Analysis Seminar.

Wednesday, 17 April 2013
4:10 p.m. in Math 311
3:30 p.m. Refreshments in Math Lounge 109

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