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1.
It is shown that for every separable Banach space X with non-separable dual, the space contains an unconditional family of size . The proof is based on Ramsey Theory for trees and finite products of perfect sets of reals. Among its consequences, it is proved that every dual Banach space has a separable quotient.  相似文献   

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We characterize spectral properties of operator cosine functions in Banach spaces in terms of the Césaro summability of two series associated to the resolvent of the corresponding infinitesimal generator.

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The main object of this presentation is to show how some simple combinatorial identities can lead to several general families of combinatorial and other series identities as well as summation formulas associated with the Fox-Wright function pΨq and various related generalized hypergeometric functions. At least one of the hypergeometric summation formulas, which is derived here in this manner, has already found a remarkable application in producing several interesting generalizations of the Karlsson-Minton summation formula. We also consider a number of other combinatorial series identities and rational sums which were proven, in recent works, by using different methods and techniques. We show that much more general results can be derived by means of certain summation theorems for hypergeometric series. Relevant connections of the results presented here with those in the aforementioned investigations are also considered.  相似文献   

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We prove that if a metric probability space with a usual concentration property embeds into a finite dimensional Banach space X, then X has a Euclidean subspace of a proportional dimension. In particular this yields a new characterization of weak cotype 2. We also find optimal lower estimates on embeddings of metric spaces with concentration properties into , generalizing estimates of Bourgain—Lindenstrauss—Milman, Carl—Pajor and Gluskin. Submitted: February 2001, Revised: August 2001.  相似文献   

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LetS be the binary tree of all sequences of 0’s and 1’s. A chain ofS is any infinite linearly ordered subset. Let be an analytic set of chains, we show that there exists a binary subtreeS’ ofS such that either all chains ofS’ lie in or no chain ofS’ lies in. As an application, we prove the following result on Banach spaces: If (x s) sɛs is a bounded sequence of elements in a Banach spaceE, there exists a subtreeS’ ofS such that for any chainβ ofS’ the sequence (x s ) sβ is either a weak Cauchy sequence or equivalent to the usuall 1 basis.  相似文献   

8.
We first introduce the notion of (p,q,r)-complemented subspaces in Banach spaces, where p,q,rN. Then, given a couple of triples {(p,q,r),(s,t,u)} in N and putting Λ=(q+rp)(t+us)−ru, we prove partially the following conjecture: For every pair of Banach spaces X and Y such that X is (p,q,r)-complemented in Y and Y is (s,t,u)-complemented in X, we have that X is isomorphic Y if and only if one of the following conditions holds:
(a)
Λ≠0, Λ divides pq and st, p=1 or q=1 or s=1 or t=1.
(b)
p=q=s=t=1 and gcd(r,u)=1.
The case {(2,1,1),(2,1,1)} is the well-known Pe?czyński's decomposition method. Our result leads naturally to some generalizations of the Schroeder-Bernstein problem for Banach spaces solved by W.T. Gowers in 1996.  相似文献   

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The notion of the bounded approximation property = BAP (resp. the uniform approximation property = UAP) of a pair [Banach space, its subspace] is used to prove that if X is a -space, Y a subspace with the BAP (resp. UAP), then the quotient X/Y has the BAP (resp. UAP). If Q: XZ is a surjection, X is a 1-space and Z is a p -space (1 ≤ p ≤ ∞), then ker Q has the UAP. A complemented subspace of a weakly sequentially complete Banach lattice has the separable complementation property = SCP. A criterion for a space with GL-l.u.st. to have the SCP is given. Spaces which are quotients of weakly sequentially complete lattices and are uncomplemented in their second duals are studied. Examples are given of spaces with the SCP which have subspaces that fail the SCP. The results are applied to spaces of measures on a compact Abelian group orthogonal to a fixed Sidon set and to Sobolev spaces of functions of bounded variation on ℝ n .  相似文献   

12.
分别对Banach空间值鞅差序列和独立随机变量序列证明了Rosenthal型不等式,所得结论揭示了Rosenthal型不等式与Banach空间的p型、q余型、p一致光滑性和q一致凸性之间的内在联系.  相似文献   

13.
We investigate the minimum value ofD =D(n) such that anyn-point tree metric space (T, ρ) can beD-embedded into a given Banach space (X, ∥·∥); that is, there exists a mappingf :TX with 1/D ρ(x,y) ≤ ∥f(x) −f(y)∥ ≤ρ(x,y) for anyx,y εT. Bourgain showed thatD(n) grows to infinity for any superreflexiveX (and this characterized super-reflexivity), and forX = p, 1 <p < ∞, he proved a quantitative lower bound of const·(log logn)min(1/2,1/p). We give another, completely elementary proof of this lower bound, and we prove that it is tight (up to the value of the constant). In particular, we show that anyn-point tree metric space can beD-embedded into a Euclidean space, with no restriction on the dimension, withD =O(√log logn). This paper contains results from my thesis [Mat89] from 1989. Since the subject of bi-Lipschitz embeddings is becoming increasingly popular, in 1997 I finally decided to publish this English version. Supported by Czech Republic Grant GAČR 0194 and by Charles University grants No. 193, 194.  相似文献   

14.
A detailed development is given of a theory of complex interpolation for families of Banach spaces which extends the well-known theory for pairs of spaces.  相似文献   

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Some examples concerning rotundity in Banach spaces   总被引:3,自引:0,他引:3  
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We deal with anti-periodic problems for differential inclusions with nonmonotone perturbations. The main tools in our study are the maximal monotone property of the derivative operator with anti-periodic conditions and the theory of pseudomonotone perturbations of maximal monotone mappings. We then apply our results to evolution hemivariational inequalities and parabolic equations with nonmonotone discontinuities, which generalize and extend previously known theorems.  相似文献   

20.
Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 55, pp. 140–145, 1991.  相似文献   

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