# 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) multiplie*r 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.

## Recommended Citation

Palacios, Lourdes, "On the multiplier algebra of certain locally m-convex algebras" (2013). *Colloquia of the Department of Mathematical Sciences*. 426.

https://scholarworks.umt.edu/mathcolloquia/426

## 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