On generalized topological divisors of zero in m-convex locally convex algebras

M-FUZZIFYING TOPOLOGICAL CONVEX SPACES

The main purpose of this paper is to introduce the compatibility of $M$-fuzzifying topologies and $M$-fuzzifying convexities, define an $M$-fuzzifying topological convex space, and give a method to generate an $M$-fuzzifying topological convex space. Some characterizations of $M$-fuzzifying topological convex spaces are presented. Finally, the notion of $M$-fuzzifying weak topologies is obtaine...

SYMMETRIC m-CONVEX ALGEBRAS WITHOUT ALGEBRAIC ZERO DIVISORS AND RESULTS OF GELFAND-MAZUR TYPE

We show that in a symmetric m-convex algebra without algebraic zero divisors, any self-adjoint and invertible element is either positive or negative. As a consequence we obtain that a symmetric m-convex algebra containing no algebraic zero divisors and for which every positive element has a positive square root is isomorphic to C + Rad(A).

m-CONVEX ALGEBRAS WITHOUT ALGEBRAIC ZERO DIVISORS AND RESULTS OF GELFAND-MAZUR TYPE

We show that in a symmetric m-convex algebra without algebraic zero divisors, any self-adjoint and invertible element is either positive or negative. As a consequence we obtain that a symmetric m-convex algebra containing no algebraic zero divisors and for which every positive element has a positive square root is isomorphic to C + Rad(A).

Notes on Locally Convex Topological Vector Spaces

Notes from a 1994–95 graduate course. Designed to supplement the topological vector space chapters of Rudin's Functional Analysis.

Some Results on Boundedness in Locally Convex Cones