The adic realizations of the ergodic actions with the homeomorphisms of the Markov compact and the ordered Bratteli diagrams
The adjoint theorem on A-spaces.
The algebra of compact operators does not have any finite-codimensional ideal
The algebra of polynomials on the space of ultradifferentiable functions
We consider the space of ultradifferentiable functions with compact supports and the space of polynomials on . A description of the space of polynomial ultradistributions as a locally convex direct sum is given.
The algebra property of the integrals of some analytic functions in the unit disk.
The algebraic dimension of linear metric spaces and Baire properties of their hyperspaces.
Answering a question of Halbeisen we prove (by two different methods) that the algebraic dimension of each infinite-dimensional complete linear metric space X equals the size of X. A topological method gives a bit more: the algebraic dimension of a linear metric space X equals |X| provided the hyperspace K(X) of compact subsets of X is a Baire space. Studying the interplay between Baire properties of a linear metric space X and its hyperspace, we construct a hereditarily Baire linear metric space...
The algebraic Riccati equation with Toeplitz matrices as coefficients.
The almost Daugavet property and translation-invariant subspaces
Let G be a metrizable, compact abelian group and let Λ be a subset of its dual group Ĝ. We show that has the almost Daugavet property if and only if Λ is an infinite set, and that has the almost Daugavet property if and only if Λ is not a Λ(1) set.
The almost lattice isometric copies of in Banach lattices
In this paper it is shown that if a Banach lattice contains a copy of , then it contains an almost lattice isometric copy of . The above result is a lattice version of the well-known result of James concerning the almost isometric copies of in Banach spaces.
The alternative Dunford-Pettis Property in the predual of a von Neumann algebra
Let A be a type II von Neumann algebra with predual A⁎. We prove that A⁎ does not have the alternative Dunford-Pettis property introduced by W. Freedman [7], i.e., there is a sequence (φₙ) converging weakly to φ in A⁎ with ||φₙ|| = ||φ|| = 1 for all n ∈ ℕ and a weakly null sequence (xₙ) in A such that φₙ(xₙ) ↛ 0. This answers a question posed in [7].
The analytic -capacity and the Cauchy integral
The angular distribution of mass by Bergman functions.
Let D = {z: |z| < 1} be the unit disk in the complex plane and denote by dA two-dimensional Lebesgue measure on D. For ε > 0 we define Σε = {z: |arg z| < ε}. We prove that for every ε > 0 there exists a δ > 0 such that if f is analytic, univalent and area-integrable on D, and f(0) = 0 thenThis problem arose in connection with a characterization by Hamilton, Reich and Strebel of extremal dilatation for quasiconformal homeomorphisms of D.
The angular distribution of mass by weighted Bergman functions.
The approximation of continuous linear functionals.
The approximation property for a pair of Banach spaces.
The approximation property of order p in locally convex spaces.
The approximation property of order (p,q) in Banach spaces.
The approximation property of some vector valued Sobolev-Slobodeckij spaces.
The arithmetic of distributions in free probability theory
We give an analytical approach to the definition of additive and multiplicative free convolutions which is based on the theory of Nevanlinna and Schur functions. We consider the set of probability distributions as a semigroup M equipped with the operation of free convolution and prove a Khintchine type theorem for the factorization of elements of this semigroup. An element of M contains either indecomposable (“prime”) factors or it belongs to a class, say I 0, of distributions without indecomposable...
The AR-Property of the spaces of closed convex sets
Let , and be the spaces of all non-empty closed convex sets in a normed linear space X admitting the Hausdorff metric topology, the Attouch-Wets topology and the Wijsman topology, respectively. We show that every component of and the space are AR. In case X is separable, is locally path-connected.