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 groups of invertible elements in C*-algebras
We describe all surjective isometries between open subgroups of the groups of invertible elements in unital C*-algebras. As a consequence the two C*-algebras are Jordan *-isomorphic if and only if the groups of invertible elements in those C*-algebras are isometric as metric spaces.
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 a function space.
Isometries of Banach Algebras Satisfying the von Neumann Inequality.
Isometries of JB-algebras.
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 Non-Commutative Lorentz Spaces.
Isometries of normed spaces
We improve the Mazur-Ulam theorem by relaxing the surjectivity condition.
Isometries of Orlicz Spaces of Vector Valued Functions.
Isometries of some F-algebras of holomorphic functions on the upper half plane
Linear isometries of N p(D) onto N p(D) are described, where N p(D), p > 1, is the set of all holomorphic functions f on the upper half plane D = {z ∈ ℂ: Im z > 0} such that supy>0 ∫ℝ lnp (1 + |(x + iy)|) dx < +∞. Our result is an improvement of the results by D.A. Efimov.
Isometries of the unitary groups in C*-algebras
We give a complete description of the structure of surjective isometries between the unitary groups of unital C*-algebras. While any surjective isometry between the unitary groups of von Neumann algebras can be extended to a real-linear Jordan *-isomorphism between the relevant von Neumann algebras, this is not the case for general unital C*-algebras. We show that the unitary groups of two C*-algebras are isomorphic as metric groups if and only if the C*-algebras are isomorphic in the sense that...
Isometries on linear -normed spaces.
Isometries on products of composition and integral operators on Bloch type space.
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 classification and lifting theorems for spaces of differentiable functions with Lipschitz conditions