In this paper, we have dened and studied a generalized form of topological vector spaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of Levine. Along with other results, it is proved that every s-topological vector space is generalized homogeneous space. Every open subspace of an s-topological vector space is...

Throughout the sequel, E denotes a reflexive real Banach space and E∗ its topological dual. We also assume that E is locally uniformly convex. This means that for each x ∈ E, with ‖x‖ = 1, and each > 0, there exists δ > 0 such that, for every y ∈ E satisfying ‖y‖ = 1 and ‖x− y‖ ≥ , one has ‖x + y‖ ≤ 2(1 − δ). Recall that any reflexive Banach space admits an equivalent norm with which it is loca...

Let X be a completely regular Hausdorff space, E a Hausdorff topological vector space, CL(E) the algebra of continuous operators on E, V a Nachbin family on X and F ⊆ CVb(X,E) a topological vector space (for a given topology). If π : X → CL(E) is a mapping and f ∈ F , let Mπ(f)(x) := π(x)f(x). In this paper we give necessary and sufficient conditions for the induced linear mapping Mπ to be a mu...

in this paper, we have dened and studied a generalized form of topological vectorspaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of levine. along with other results, it is provedthat every s-topological vector space is generalized homogeneous space. every open subspaceof an s-topological vector space is ...

best approximation results provide an approximate solution to the fixed point equation $tx=x$, when the non-self mapping $t$ has no fixed point. in particular, a well-known best approximation theorem, due to fan cite{5}, asserts that if $k$ is a nonempty compact convex subset of a hausdorff locally convex topological vector space $e$ and $t:krightarrow e$ is a continuous mapping, then there exi...

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

The Schauder-Tychonoff theorem states that a continuous function from a compact convex subset of a locally convex topological vector space into itself must have a fixed point ([1, Chapter V, 10.5], or [2]). Using this theorem, we obtain here a stronger result, stating that a map from such a set into the surrounding vector space has a fixed point if the directions in which the points are moved s...

Let A be a partial *-algebra endowed with a topology that makes it into a locally convex topological vector space AA]. Then A is called a topological partial *-algebra if it satisses a number of conditions, which all amount to require that the topology ts with the multiplier structure of A. Besides the obvious cases of topological quasi *-algebras and CQ*-algebras, we examine several classes of...

We provide a rule to calculate the subdifferential of the pointwise supremum of an arbitrary family of convex functions defined on a real locally convex topological vector space. Our formula is given exclusively in terms of the data functions, and does not require any assumption either on the index set on which the supremum is taken or on the involved functions. Some other calculus rules, namel...