All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 60 Next

Displaying 1181 – 1200 of 3251

Showing per page

Isometries of the unitary groups in C*-algebras

Osamu Hatori (2014)

Studia Mathematica

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...

Isomorphic and isometric copies of ℓ ∞ ( Γ ) in duals of Banach spaces and Banach lattices

Marek Wójtowicz (2006)

Commentationes Mathematicae Universitatis Carolinae

Let X and E be a Banach space and a real Banach lattice, respectively, and let Γ denote an infinite set. We give concise proofs of the following results: (1) The dual space X * contains an isometric copy of c 0 iff X * contains an isometric copy of ℓ ∞ , and (2) E * contains a lattice-isometric copy of c 0 ( Γ ) iff E * contains a lattice-isometric copy of ℓ ∞ ( Γ ) .

Isomorphic Schauder decompositions in certain Banach spaces

Vitalii Marchenko (2014)

Open Mathematics

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,...

Isomorphisms of AC(σ) spaces

Ian Doust, Michael Leinert (2015)

Studia Mathematica

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

Jiankui Li, Zhidong Pan (2008)

Studia Mathematica

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 E i such that ( E i ) ₋ ≠ X , E i ⊆ E i + 1 , and ⋁ i = 1 ∞ E i = X then every automorphism of algℒ is quasi-spatial.

Isospectrality for quantum toric integrable systems

Laurent Charles, Álvaro Pelayo, San Vũ Ngoc (2013)

Annales scientifiques de l'École Normale Supérieure

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...

Iterates and the boundary behavior of the Berezin transform

Jonathan Arazy, Miroslav Engliš (2001)

Annales de l’institut Fourier

Let μ be a measure on a domain Ω in ℂ n such that the Bergman space of holomorphic functions in L 2 ( Ω , μ ) possesses a reproducing kernel K ( x , y ) and K ( x , x ) > 0 ∀ x ∈ Ω . The Berezin transform associated to μ is the integral...

Jacobi matrices on trees

Agnieszka M. Kazun, Ryszard Szwarc (2010)

Colloquium Mathematicae

Symmetric Jacobi matrices on one sided homogeneous trees are studied. Essential selfadjointness of these matrices turns out to depend on the structure of the tree. If a tree has one end and infinitely many origin points the matrix is always essentially selfadjoint independently of the growth of its coefficients. In case a tree has one origin and infinitely many ends, the essential selfadjointness is equivalent to that of an ordinary Jacobi matrix obtained by restriction to the so called radial functions....

Joint subnormality of n-tuples and C₀-semigroups of composition operators on L²-spaces

Piotr Budzyński, Jan Stochel (2007)

Studia Mathematica

Joint subnormality of a family of composition operators on L²-space is characterized by means of positive definiteness of appropriate Radon-Nikodym derivatives. Next, simplified positive definiteness conditions guaranteeing joint subnormality of a C₀-semigroup of composition operators are supplied. Finally, the Radon-Nikodym derivatives associated to a jointly subnormal C₀-semigroup of composition operators are shown to be the Laplace transforms of probability measures (modulo a C₀-group of scalars)...

Currently displaying 1181 – 1200 of 3251