On weighted spaces without a fundamental sequence of bounded sets.
On Well-Located Subspaces of Distribution-Spaces.
On -valued sequence spaces.
On -nuclearity
On -Chebyshev subspaces of Banach spaces.
One-parameter semigroups of operators on Lc-embedded spaces.
Open mapping theorem and inversion theorem for γ-paraconvex multivalued mappings and applications
We extend the open mapping theorem and inversion theorem of Robinson for convex multivalued mappings to γ-paraconvex multivalued mappings. Some questions posed by Rolewicz are also investigated. Our results are applied to obtain a generalization of the Farkas lemma for γ-paraconvex multivalued mappings.
Open mapping theorems in topological spaces
Open partial isometries and positivity in operator spaces
We first study positivity in C*-modules using tripotents ( = partial isometries) which are what we call open. This is then used to study ordered operator spaces via an "ordered noncommutative Shilov boundary" which we introduce. This boundary satisfies the usual universal diagram/property of the noncommutative Shilov boundary, but with all the arrows completely positive. Because of their independent interest, we also systematically study open tripotents and their properties.
Open problems in theory of metric linear spaces
Open Subsets of LF-spaces
Let F = ind lim Fₙ be an infinite-dimensional LF-space with density dens F = τ ( ≥ ℵ ₀) such that some Fₙ is infinite-dimensional and dens Fₙ = τ. It is proved that every open subset of F is homeomorphic to the product of an ℓ₂(τ)-manifold and (hence the product of an open subset of ℓ₂(τ) and ). As a consequence, any two open sets in F are homeomorphic if they have the same homotopy type.
Openness of linear mappings in -spaces
Opérations sur les espaces vectoriels topologiques métrisables
Operator and function spaces which are K-analytic
Operators commuting with the shift on sequence spaces.
Optimization of Convex function on w*-compact sets.
Order bounded orthosymmetric bilinear operator
It is proved by an order theoretical and purely algebraic method that any order bounded orthosymmetric bilinear operator where and are Archimedean vector lattices is symmetric. This leads to a new and short proof of the commutativity of Archimedean almost -algebras.
Order boundedness and weak compactness of the set of quasi-measure extensions of a quasi-measure
Let and be algebras of subsets of a set with , and denote by the set of all quasi-measure extensions of a given quasi-measure on to . We give some criteria for order boundedness of in , in the general case as well as for atomic . Order boundedness implies weak compactness of . We show that the converse implication holds under some assumptions on , and or alone, but not in general.
Order continuous linear functionals on non-locally convex Orlicz spaces
The space of all order continuous linear functionals on an Orlicz space defined by an arbitrary (not necessarily convex) Orlicz function is described.
Order continuous seminorms and weak compactness in Orlicz spaces.
Let L-phi be an Orlicz space defined by a Young function phi over a sigma-finite measure space, and let phi* denote the complementary function in the sense of Young. We give a characterization of the Mackey topology tau(L*,L-phi*) in terms of some family of norms defined by some regular Young functions. Next we describe order continuous (=absolutely continuous) Riesz seminorms on L-phi, and obtain a criterion for relative sigma(L-phi,L-phi*)-compactness in L-phi. As an application we get a representation...