On embeddings for classes of functions with generalized smoothness on metric spaces.
On embeddings of C₀(K) spaces into C₀(L,X) spaces
For a locally compact Hausdorff space K and a Banach space X let C₀(K, X) denote the space of all continuous functions f:K → X which vanish at infinity, equipped with the supremum norm. If X is the scalar field, we denote C₀(K, X) simply by C₀(K). We prove that for locally compact Hausdorff spaces K and L and for a Banach space X containing no copy of c₀, if there is an isomorphic embedding of C₀(K) into C₀(L,X), then either K is finite or |K| ≤ |L|. As a consequence, if there is an isomorphic embedding...
On embeddings of function classes defined by constructive characteristics
In this paper we study embedding theorems for function classes which are subclasses of , 1 ≤ p ≤ ∞. To define these classes, we use the notion of best trigonometric approximation as well as that of a (λ,β)-derivative, which is the generalization of a fractional derivative. Estimates of best approximations of transformed Fourier series are obtained.
On equilibrium point in topological vector spaces
On equivalence of K- and J-methods for (n+1)-tuples of Banach spaces
It is shown that the main results of the theory of real interpolation, i.e. the equivalence and reiteration theorems, can be extended from couples to a class of (n+1)-tuples of Banach spaces, which includes (n+1)-tuples of Banach function lattices, Sobolev and Besov spaces. As an application of our results, it is shown that Lions' problem on interpolation of subspaces and Semenov's problem on interpolation of subcouples have positive solutions when all spaces are Banach function lattices or their...
On equivalence of super log Sobolev and Nash type inequalities
We prove the equivalence of Nash type and super log Sobolev inequalities for Dirichlet forms. We also show that both inequalities are equivalent to Orlicz-Sobolev type inequalities. No ultracontractivity of the semigroup is assumed. It is known that there is no equivalence between super log Sobolev or Nash type inequalities and ultracontractivity. We discuss Davies-Simon's counterexample as the borderline case of this equivalence and related open problems.
On equivalent strictly G-convex renormings of Banach spaces
We study strictly G-convex renormings and extensions of strictly G-convex norms on Banach spaces. We prove that ℓω(Γ) space cannot be strictly G-convex renormed given Γ is uncountable and G is bounded and separable.
On Ergodic Flows and the Isomorphism of Factors.
On ergodic properties of convolution operators associated with compact quantum groups
Recent results of M. Junge and Q. Xu on the ergodic properties of the averages of kernels in noncommutative -spaces are applied to the analysis of almost uniform convergence of operators induced by convolutions on compact quantum groups.
On ergodicity for operators with bounded resolvent in Banach spaces
We prove results on ergodicity, i.e. on the property that the space is a direct sum of the kernel of an operator and the closure of its range, for closed linear operators A such that is uniformly bounded for all α > 0. We consider operators on Banach spaces which have the property that the space is complemented in its second dual space by a projection P. Results on ergodicity are obtained under a norm condition ||I - 2P|| ||I - Q|| < 2 where Q is a projection depending on the operator A....
On essential sets of function algebras in terms of their orthogonal measures
In the present note, we characterize the essential set of a function algebra defined on a compact Hausdorff space in terms of its orthogonal measures on .
On essentially incomparable Banach spaces.
On estimates of normal structure coefficients of Banach spaces.
On estimates of the generalized Jordan--von Neumann constant of Banach spaces.
On estimating the diffusion coefficient [Abstract of thesis]
On exact sequences of quojections.
We give some general exact sequences for quojections from which many interesting representation results for standard twisted quojections can be deduced. Then the methods are also generalized to the case of nuclear Fréchet spaces.
On exhaustive vector measures.
On existence of the weak solution for non-linear partial differential equations of elliptic type. II.
On exposed semigroup homomorphisms.
On extendability of invariant distributions
In this paper sufficient conditions are given in order that every distribution invariant under a Lie group extend from the set of orbits of maximal dimension to the whole of the space. It is shown that these conditions are satisfied for the n-point action of the pure Lorentz group and for a standard action of the Lorentz group of arbitrary signature.