arXiv math/96122101996-12-31math.FA

The Pelczynski property for tight subspaces

Scott F. Saccone

英文摘要：

We show that if X is a tight subspace of C(K) then X has the Pelczynski property and X^* is weakly sequentially complete. We apply this result to the space U of uniformly convergent Taylor series on the unit circle and using a minimal amount of Fourier theory prove a theorem of Bourgain, namely that U has the Pelczynski property and U^* is weakly sequentially complete. Using separate methods, we prove U and U^* have the Dunford-Pettis property. Some results concerning pointwise bounded approximation are proved for tight uniform algebras. We use tightness and the Pelczynski property sto make a remark about inner functions on strictly pseudoconvex domains in C^n.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Quotients of Banach spaces with the Daugavet property

We consider a general concept of Daugavet property with respect to a norming subspace. This concept covers both the usual Daugavet property and its weak$^*$ analogue. We introduce and study analogues for narrow operators and rich subspaces in this general setting and apply the results to show that a quotient of $L_1[0,1]$ over an $\ell_1$-subspace can fail the Daugavet property. The latter answers a question posed to us by A. Pelczynski in the negative.

2008-06-11math.FA

Tight embedding of subspaces of $L_p$ in $\ell_p^n$ for even $p$

Using a recent result of Batson, Spielman and Srivastava, We obtain a tight estimate on the dimension of $\ell_p^n$, $p$ an even integer, needed to almost isometrically contain all $k$-dimensional subspaces of $L_p$.

2010-09-06math.FA

Random fusion frames are nearly equiangular and tight

This paper demonstrates that random, independently chosen equi-dimensional subspaces with a unitarily invariant distribution in a real Hilbert space provide nearly tight, nearly equiangular fusion frames. The angle between a pair of subspaces is measured in terms of the Hilbert-Schmidt inner product of the corresponding orthogonal projections. If the subspaces are selected at random, then a measure concentration argument shows that these inner products concentrate near an average value. Overwhelming success probability for near tightness and equiangularity is guaranteed if the dimension of the…

2013-03-23math.FA

Tight projections of frames on infinite dimensional Hilbert spaces

We characterize the frames on an infinite dimensional separable Hilbert space that can be projected to a tight frame for an infinite dimensional subspace. A result of Casazza and Leon states that an arbitrary frame for a 2N- or (2N-1)-dimensional Hilbert space can be projected to a tight frame for an N-dimensional subspace. Surprisingly, we demonstrate a large class of frames for infinite dimensional Hilbert spaces which cannot be projected to a tight frame for any infinite dimensional subspace.

2012-11-14math.FA

Robust Dimension Reduction, Fusion Frames, and Grassmannian Packings

We consider estimating a random vector from its noisy projections onto low dimensional subspaces constituting a fusion frame. A fusion frame is a collection of subspaces, for which the sum of the projection operators onto the subspaces is bounded below and above by constant multiples of the identity operator. We first determine the minimum mean-squared error (MSE) in linearly estimating the random vector of interest from its fusion frame projections, in the presence of white noise. We show that MSE assumes its minimum value when the fusion frame is tight. We then analyze the robustness of the …

2007-09-14math.FA

A $c_0$ saturated Banach space with tight structure

It is shown that variants of the HI methods could yield objects closely connected to the classical Banach spaces. Thus we present a new $c_0$ saturated space, denoted as $\mathfrak{X}_0$, with rather tight structure. The space $\mathfrak{X}_0$ is not embedded into a space with an unconditional basis and its complemented subspaces have the following structure. Everyone is either of type I, namely, contains an isomorph of $\mathfrak{X}_0$ itself or else is isomorphic to a subspace of $c_0$ (type II). Furthermore for any analytic decomposition of $\mathfrak{X}_0$ into two subspaces one is of type…

2010-12-13math.FA

更多相关论文收起更多论文

Operators in tight by support Banach spaces

We answer the question of W.T. Gowers, giving an example of a bounded operator on a subspace of Gowers unconditional space which is not a strictly singular perturbation of a restriction of a diagonal operator. We make some observations on operators in arbitrary tight by support Banach space, showing in particular that in such space no two isomorphic infinitely dimensional subspaces form a direct sum.

2015-06-11math.FA

Banach空间中的紧-极小二分性

Tight-minimal dichotomies in Banach spaces

本文推广Ferenczi-Rosendal方法，证明带容许块系统的Banach空间包含A-紧或A-极小的无穷维子空间，并由此得到基的子序列二分性及紧性的Baire范畴解释。

2023-12-01math.FA

Subspace concentration of dual curvature measures

We prove a tight subspace concentration inequality for the dual curvature measures of a symmetric convex body.

2016-04-23math.FAmath.MG

Necessary subspace concentration conditions for the even dual Minkowski problem

We prove tight subspace concentration inequalities for the dual curvature measures $\widetilde{\mathrm{C}}_q(K,\cdot)$ of an $n$-dimensional origin-symmetric convex body for $q\geq n+1$. This supplements former results obtained in the range $q\leq n$.

2017-03-30math.FAmath.MG

Tight Bounds for the Subspace Sketch Problem with Applications

In the subspace sketch problem one is given an $n\times d$ matrix $A$ with $O(\log(nd))$ bit entries, and would like to compress it in an arbitrary way to build a small space data structure $Q_p$, so that for any given $x \in \mathbb{R}^d$, with probability at least $2/3$, one has $Q_p(x)=(1\pmε)\|Ax\|_p$, where $p\geq 0$, and where the randomness is over the construction of $Q_p$. The central question is: How many bits are necessary to store $Q_p$? This problem has applications to the communication of approximating the number of non-zeros in a matrix product, the size of coresets in projectiv…

2019-10-12cs.DSmath.FA