The concept of convex-compactness, weaker than the classical notion of compactness, is introduced and discussed. It is shown that a large class of convex subsets of topological vector spaces shares this property and that is can be used in lieu of compactness in a variety of cases. In particular, we show that bounded-in-probability, convex and closed subsets of the space L+(Ω,F , P) of finite-va...

In this work we introduce a theory of stochastic integration with respect to general cylindrical semimartingales defined on locally convex space $\Phi$. Our construction the integral is based tensor products topological vector spaces and property good integrators real-valued semimartingales. This further developed in case where $\Phi$ complete, barrelled, nuclear space, obtain complete descript...

A topological description of various generalized function algebras over corresponding basic locally convex algebras is given. The framework consists of algebras of sequences with appropriate ultra(pseudo)metrics defined by sequences of exponential weights. Such an algebra with embedded Dirac’s delta distribution induces discrete topology on the basic space. This result is in analogy to Schwartz...

A topological description of various generalized function algebras over corresponding basic locally convex algebras is given. The framework consists of algebras of sequences with appropriate ultra(pseudo)metrics defined by sequences of exponential weights. Such an algebra with embedded Dirac’s delta distribution induces discrete topology on the basic space. This result is in analogy to Schwartz...

The main use of ∗-autonomous categories is in the semantic study of Linear Logic. For this reason, it is thus natural to look for a ∗-autonomous category of locally convex topological vector spaces (tvs). On one hand, Linear Logic inherits its semantics from Linear Algebra, and it is thus natural to build models of Linear Logic from vector spaces [3,5,6,4]. On the other hand, denotational seman...

in [1,2,3], a. c. baker and j.w. baker studied the subspace ma(s) of the convolution measure algebra m, (s) of a locally compact semigroup. h. dzinotyiweyi in [5,7] considers an analogous measure space on a large class of c-distinguished topological semigroups containing all completely regular topological semigroups. in this paper, we extend the definitions to study the weighted semigroup algeb...

Let E be a topological vector space and X be a non-empty subset of E. Let S : X → 2X and T : X → 2E be two maps. Then the generalized quasi-variational inequality (GQVI) problem is to find a point ŷ ∈ S(ŷ) and a point ŵ ∈ T (ŷ) such that Re〈ŵ, ŷ − x〉 ≤ 0 for all x ∈ S(ŷ). We shall use Chowdhury and Tan’s 1996 generalized version of Ky Fan’s minimax inequality as a tool to obtain some general th...

This paper extends the known results on the equivalence between market completeness and the uniqueness of martingale measures for finite asset economies, to the infinite asset case. Our arguments employ results from the theory of linear operators between locally convex topological vector spaces. This theory of linear operators provides an operational approach to the issue of completeness and un...