RT journal article
T1 Topological modules geometry
A1 García Pacheco, Francisco Javier
A2 Matemáticas
K1 C*-algebra
K1 Effect algebra
K1 Topological module
K1 Topological ring
AB The extremal structure of zero-neighbourhoods of a topological module is analyzed reaching unexpected conclusions when the module topology is not Hausdorff. These results motivate us to introduce the notion of metric modules, which are modules endowed with a translation-invariant metric, turning them into an (additive) topological group. We study the central and diametral points of additively symmetric subsets and find examples of convex sets which are not symmetric translates (translates of addivitely symmetric subsets). As a consequence of all of these, it seems natural to transport the well-known Bishop-Phelps property from the category of real topological vector spaces to general topological modules over topological rings. Then we stick to particular topological rings, the unital C∗ -algebras, showing that the subset of positive elements lying below the unity is an effect algebra. We also prove that every continuous linear operator on a Hausdorff locally convex topological vector space that commutes with all continuous linear projections of one-dimensional range is a multiple of the identity. Finally, we discuss how to transport the previous result to C∗ -algebras.
PB Springer
SN 1072-3374
YR 2023
FD 2023-12-27
LK http://hdl.handle.net/10498/31383
UL http://hdl.handle.net/10498/31383
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 12-nov-2026