Isometries of Orlicz Spaces of Vector Valued Functions.
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 Irreducible Triangular Operator Algebras.
Isometries on products of composition and integral operators on Bloch type space.
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 classification and lifting theorems for spaces of differentiable functions with Lipschitz conditions
Isomorphic embeddings of some generalized power series spaces
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,...
Isomorphic type of the space of smooth functions determined by a finite family of differential operators.
Isomorphismes bicroissants des cônes convexes.
Isomorphisms of AC(σ) spaces
Analogues of the classical Banach-Stone theorem for spaces of continuous functions are studied in the context of the spaces of absolutely continuous functions introduced by Ashton and Doust. We show that if AC(σ₁) is algebra isomorphic to AC(σ₂) then σ₁ is homeomorphic to σ₂. The converse however is false. In a positive direction we show that the converse implication does hold if the sets σ₁ and σ₂ are confined to a restricted collection of compact sets, such as the set of all simple polygons.
Isomorphisms of some reflexive algebras
Suppose ℒ₁ and ℒ₂ are subspace lattices on complex separable Banach spaces X and Y, respectively. We prove that under certain lattice-theoretic conditions every isomorphism from algℒ₁ to algℒ₂ is quasi-spatial; in particular, if a subspace lattice ℒ of a complex separable Banach space X contains a sequence such that , , and then every automorphism of algℒ is quasi-spatial.
Isoperimetric inequalities for some nonlinear eigenvalue problems.
Isoperimetry between exponential and Gaussian.
Isospectrality for quantum toric integrable systems
We give a full description of the semiclassical spectral theory of quantum toric integrable systems using microlocal analysis for Toeplitz operators. This allows us to settle affirmatively the isospectral problem for quantum toric integrable systems: the semiclassical joint spectrum of the system, given by a sequence of commuting Toeplitz operators on a sequence of Hilbert spaces, determines the classical integrable system given by the symplectic manifold and commuting Hamiltonians. This type of...
Iterated series and the Hellinger-Toeplitz theorem.
We show that an iterated double series condition due to Antosik implies the uniform convergence of the double series. An application of Antosik's condition is given to the derivation of a vector form of the Hellinger-Toeplitz theorem.
Iterates and the boundary behavior of the Berezin transform
Let be a measure on a domain in such that the Bergman space of holomorphic functions in possesses a reproducing kernel and . The Berezin transform associated to is the integral...
Iterates of a class of discrete linear operators via contraction principle
In this paper we are concerned with a general class of positive linear operators of discrete type. Based on the results of the weakly Picard operators theory our aim is to study the convergence of the iterates of the defined operators and some approximation properties of our class as well. Some special cases in connection with binomial type operators are also revealed.
Iterates of maps which are non-expansive in Hilbert's projective metric
The cycle time of an operator on gives information about the long term behaviour of its iterates. We generalise this notion to operators on symmetric cones. We show that these cones, endowed with either Hilbert’s projective metric or Thompson’s metric, satisfy Busemann’s definition of a space of non- positive curvature. We then deduce that, on a strictly convex symmetric cone, the cycle time exists for all maps which are non-expansive in both these metrics. We also review an analogue for the Hilbert...
Iterates of Volterra operators and indeterminate forms.