Topological conditions for bound-2 isomorphisms of C(X)
We establish the topological relationship between compact Hausdorff spaces X and Y equivalent to the existence of a bound-2 isomorphism of the sup norm Banach spaces C(X) and C(Y).
Topological dual of with application to stochastic systems on Hilbert space
In this paper, we prove that the topological dual of the Banach space of bounded measurable functions with values in the space of nuclear operators, furnished with the natural topology, is isometrically isomorphic to the space of finitely additive linear operator-valued measures having bounded variation in a Banach space containing the space of bounded linear operators. This is then applied to a stochastic structural control problem. An optimal operator-valued measure, considered as the structural...
Topological dual of non-locally convex Orlicz-Bochner spaces
Let be an Orlicz-Bochner space defined by an Orlicz function taking only finite values (not necessarily convex) over a -finite atomless measure space. It is proved that the topological dual of can be represented in the form: , where and denote the order continuous dual and the singular dual of respectively. The spaces , and are examined by means of the H. Nakano’s theory of conjugate modulars. (Studia Mathematica 31 (1968), 439–449). The well known results of the duality theory...
Topological duals of some paranormed sequence spaces.
Topological groups and convex sets homeomorphic to non-separable Hilbert spaces
Let X be a topological group or a convex set in a linear metric space. We prove that X is homeomorphic to (a manifold modeled on) an infinite-dimensional Hilbert space if and only if X is a completely metrizable absolute (neighborhood) retract with ω-LFAP, the countable locally finite approximation property. The latter means that for any open cover of X there is a sequence of maps (f n: X → X)nεgw such that each f n is -near to the identity map of X and the family f n(X)n∈ω is locally finite...
Topological imbedding of Laplace distributions in Laplace hyperfunctions [Book]
Topological localization in Fréchet algebras.
Topological methods of investigation of operator equations and nonlinear boundary value problems
Topological modules over strictly minimal topological rings
We study the validity of two basic results of the classical theory of topological vector spaces in the context of topological modules.
Topological open problems in the geometry of Banach spaces.
Topological orbit equivalence and C*-crossed products.
Topological proper separation theorems
Topological properties and matrix transformations of certain ordered generalized sequence spaces.
Topological Properties of Real Normed Space
In this article, we formalize topological properties of real normed spaces. In the first part, open and closed, density, separability and sequence and its convergence are discussed. Then we argue properties of real normed subspace. Then we discuss linear functions between real normed speces. Several kinds of subspaces induced by linear functions such as kernel, image and inverse image are considered here. The fact that Lipschitz continuity operators preserve convergence of sequences is also refered...
Topological quasi *-algebras and the time evolution of systems
We give here a survey of some recent results on applications of topological quasi *-algebras to the analysis of the time evolution of quantum systems with infinitely many degrees of freedom.
Topological radicals, I. Basic properties, tensor products and joint quasinilpotence
Topological rings of sets and the theory of vector measures [Book]
Topological semivector spaces: convexity and fixed point theory.
Topological tensor products and asymptotic developments
Topological tensor products of a Fréchet-Schwartz space and a Banach space
We exhibit examples of countable injective inductive limits E of Banach spaces with compact linking maps (i.e. (DFS)-spaces) such that is not an inductive limit of normed spaces for some Banach space X. This solves in the negative open questions of Bierstedt, Meise and Hollstein. As a consequence we obtain Fréchet-Schwartz spaces F and Banach spaces X such that the problem of topologies of Grothendieck has a negative answer for . This solves in the negative a question of Taskinen. We also give...