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Displaying 5081 –
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The relationships between the JB*-triple structure of a complex spin factor S and the structure of the Hilbert space H associated to S are discussed. Every surjective linear isometry L of S can be uniquely represented in the form L(x) = mu.U(x) for some conjugation commuting unitary operator U on H and some mu belonging to C, |mu|=1. Automorphisms of S are characterized as those linear maps (continuity not assumed) that preserve minimal tripotents in S and the orthogonality relations among them.
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.
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.
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.
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.
We improve the Mazur-Ulam theorem by relaxing the surjectivity condition.
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.
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...
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 .
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