On classifying involutive locally $m$-convex algebras, via cones

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.

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

Relating Homogeneous Cones and Positive Definite Cones via T-Algebras

T -algebras are nonassociative algebras defined by Vinberg in the early 1960s for the purpose of studying homogeneous cones. Vinberg defined a cone K(A) for each T -algebra A and proved that every homogeneous cone is isomorphic to one such K(A). We relate each T -algebra A with a space of linear operators in such a way that K(A) is isomorphic to the cone of positive definite self-adjoint operat...