57 research outputs found
Coarse and uniform embeddings between Orlicz sequence spaces
We give an almost complete description of the coarse and uniform
embeddability between Orlicz sequence spaces. We show that the embeddability
between two Orlicz sequence spaces is in most cases determined only by the
values of their upper Matuszewska-Orlicz indices. On the other hand, we present
examples which show that sometimes the embeddability is not determined by the
values of these indices.Comment: 12 pages. This is the final version. To appear in Mediterr. J. Mat
Positive definite distributions and normed spaces
AbstractWe answer a question of Alex Koldobsky. We show that for each −∞<p<2 and each n⩾3−p there is a normed space X of dimension n which embeds in Ls if and only if −n<s⩽p
Remarks on the Central Limit Theorem for Non-Convex Bodies
In this note, we study possible extensions of the Central Limit Theorem for
non-convex bodies. First, we prove a Berry-Esseen type theorem for a certain
class of unconditional bodies that are not necessarily convex. Then, we
consider a widely-known class of non-convex bodies, the so-called p-convex
bodies, and construct a counter-example for this class
Reflexive representability and stable metrics
It is well-known that a topological group can be represented as a group of
isometries of a reflexive Banach space if and only if its topology is induced
by weakly almost periodic functions (see
\cite{Shtern:CompactSemitopologicalSemigroups},
\cite{Megrelishvili:OperatorTopologies} and
\cite{Megrelishvili:TopologicalTransformations}). We show that for a metrisable
group this is equivalent to the property that its metric is uniformly
equivalent to a stable metric in the sense of Krivine and Maurey (see
\cite{Krivine-Maurey:EspacesDeBanachStables}). This result is used to give a
partial negative answer to a problem of Megrelishvili
Spectra of weighted algebras of holomorphic functions
We consider weighted algebras of holomorphic functions on a Banach space. We
determine conditions on a family of weights that assure that the corresponding
weighted space is an algebra or has polynomial Schauder decompositions. We
study the spectra of weighted algebras and endow them with an analytic
structure. We also deal with composition operators and algebra homomorphisms,
in particular to investigate how their induced mappings act on the analytic
structure of the spectrum. Moreover, a Banach-Stone type question is addressed.Comment: 25 pages Corrected typo
Orthogonalities and functional equations
In this survey we show how various notions of orthogonality appear in the theory of functional equations. After introducing some orthogonality relations, we give examples of functional equations postulated for orthogonal vectors only. We show their solutions as well as some applications. Then we discuss the problem of stability of some of them considering various aspects of the problem. In the sequel, we mention the orthogonality equation and the problem of preserving orthogonality. Last, but not least, in addition to presenting results, we state some open problems concerning these topics. Taking into account the big amount of results concerning functional equations postulated for orthogonal vectors which have appeared in the literature during the last decades, we restrict ourselves to the most classical equations
Isometric embeddings and universal spaces
This work has been completed during the Cáceres Conference in September 2006.We show that if a separable Banach space contains isometric copies of every strictly convex separable Banach space, then actually contains an isometric copy of every separable Banach space. We prove that if is any separable Banach space of dimension at least 2, then the collection of separable Banach spaces which contain an isometric copy of is analytic non Borel.peerReviewe
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