Some applications of the open mapping theorem in locally convex cones

Egoroff Theorem for Operator-Valued Measures in Locally Convex Cones

In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...

Some Results on Boundedness in Locally Convex Cones

Bornological Completion of Locally Convex Cones

In this paper, firstly, we obtain some new results about bornological convergence in locally convex cones (which was studied in [1]) and then we introduce the concept of bornological completion for locally convex cones. Also, we prove that the completion of a bornological locally convex cone is bornological. We illustrate the main result by an example.

Locally convex cones and the Schröder-Simpson Theorem

At MFPS 23 at Birmingham, Schröder and Simpson had announced a result that I did not absorb at the time. A special case of that theorem for stably compact spaces was announced by Cohen, Escardo and the author shortly afterwards. I did not believe in the theorem of Schröder and Simpson until I saw a proof that they showed to me in detail during a visit to Edinburgh. At the New Interactions Works...

some results on boundedness in locally convex cones