Isometries between C*-algebras
Isometries between groups of invertible elements in Banach algebras
We show that if T is an isometry (as metric spaces) from an open subgroup of the group of invertible elements in a unital semisimple commutative Banach algebra A onto a open subgroup of the group of invertible elements in a unital Banach algebra B, then is an isometrical group isomorphism. In particular, extends to an isometrical real algebra isomorphism from A onto B.
Isometries between spaces of weighted holomorphic functions
We study isometries between spaces of weighted holomorphic functions. We show that such isometries have a canonical form determined by a group of homeomorphisms of a distinguished subset of the range and domain. A number of invariants for these isometries are determined. For specific families of weights we classify the form isometries can take.
Isometries of Musielak-Orlicz spaces II
A characterization of isometries of complex Musielak-Orlicz spaces is given. If is not a Hilbert space and is a surjective isometry, then there exist a regular set isomorphism τ from (T,Σ,μ) onto itself and a measurable function w such that U(f) = w ·(f ∘ τ) for all . Isometries of real Nakano spaces, a particular case of Musielak-Orlicz spaces, are also studied.
Isometries of normed spaces
We improve the Mazur-Ulam theorem by relaxing the surjectivity condition.
Isometries on linear -normed spaces.
Isométries positives et propriétés ergodiques de quelques espaces de Banach
Isomorphic and isometric copies of in duals of Banach spaces and Banach lattices
Let and be a Banach space and a real Banach lattice, respectively, and let denote an infinite set. We give concise proofs of the following results: (1) The dual space contains an isometric copy of iff contains an isometric copy of , and (2) contains a lattice-isometric copy of iff contains a lattice-isometric copy of .
Isomorphic characterizations of Hilbert spaces by orthogonal series with vector valued coefficients
Isomorphic characterizations of inner product spaces by orthogonal series with vector valued coefficients
Isomorphic properties in spaces of compact operators
We introduce the definition of -limited completely continuous operators, . The question of whether a space of operators has the property that every -limited subset is relative compact when the dual of the domain and the codomain have this property is studied using -limited completely continuous evaluation operators.
Isomorphic Schauder decompositions in certain Banach spaces
We extend a theorem of Kato on similarity for sequences of projections in Hilbert spaces to the case of isomorphic Schauder decompositions in certain Banach spaces. To this end we use ℓψ-Hilbertian and ∞-Hilbertian Schauder decompositions instead of orthogonal Schauder decompositions, generalize the concept of an orthogonal Schauder decomposition to the case of Banach spaces and introduce the class of Banach spaces with Schauder-Orlicz decompositions. Furthermore, we generalize the notions of type,...
Isomorphically isometric probabilistic normed linear spaces.
Probabilistic normed linear spaces (briefly PNL spaces) were first studied by A. N. Serstnev in [1]. His definition was motivated by the definition of probabilistic metric spaces (PM spaces) which were introduced by K. Menger and subsequebtly developed by A. Wald, B. Schweizer, A. Sklar and others.In a previuos paper [2] we studied the relationship between two important classes of PM spaces, namely E-spaces and pseudo-metrically generated PM spaces. We showed that a PM space is pseudo-metrically...
Isomorphism of certain weak spaces
It is shown that the weak spaces , and are isomorphic as Banach spaces.
Isomorphism theorems for some parabolic initial-boundary value problems in Hörmander spaces
In Hörmander inner product spaces, we investigate initial-boundary value problems for an arbitrary second order parabolic partial differential equation and the Dirichlet or a general first-order boundary conditions. We prove that the operators corresponding to these problems are isomorphisms between appropriate Hörmander spaces. The regularity of the functions which form these spaces is characterized by a pair of number parameters and a function parameter varying regularly at infinity in the sense...
Isomorphismes entre espaces
Isomorphisms and generalized derivations in proper -algebras.
Iteration of ultraproducts of locally convex spaces.
Iterations converging to distinct solutions of some nonlinear operator equations in Banach space.