arXiv 0807.23922008-07-15math.FA

Saturated extensions, the attractors method and Hereditarily James Tree Space

Spiros A. Argyros, Alexander D. Arvanitakis, Andreas G. Tolias

英文摘要：

In the present work we provide a variety of examples of HI Banach spaces containing no reflexive subspace and we study the structure of their duals as well as the spaces of their linear bounded operators. Our approach is based on saturated extensions of ground sets and the method of attractors.

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

Variants of the James Tree space

Recently, W. Cuellar Carrera, N. de Rancourt, and V. Ferenczi introduced the notion of $d_2$-hereditarily indecomposable Banach spaces, i.e., non-Hilbertian spaces that do not contain the direct sum of any two non-Hilbertian subspaces. They posed the question of the existence of such spaces that are $\ell_2$-saturated. Motivated by this question, we define and study two variants $JT_{2,p}$ and $JT_G$ of the James Tree space $JT$. They are meant to be classical analogues of a future space that will affirmatively answer the aforementioned question.

2021-01-18math.FA

The cofinal property of the Reflexive Indecomposable Banach spaces

It is shown that every separable reflexive Banach space is a quotient of a reflexive Hereditarily Indecomposable space, which yields that every separable reflexive Banach is isomorphic to a subspace of a reflexive Indecomposable space. Furthermore, every separable reflexive Banach space is a quotient of a reflexive complementably $\ell_p$ saturated space with $1<p<\infty$ and of a $c_0$ saturated space.

2010-03-03math.FA

A Banach space dichotomy for quotients of subspaces

A Banach space $X$ with a Schauder basis is defined to have the restricted quotient hereditarily indecomposable (QHI) property if $X/Y$ is hereditarily indecomposable (HI) for any infinite codimensional subspace $Y$ with a successive finite-dimensional decomposition on the basis of $X$. A reflexive space with the restricted QHI property is in particular HI, has HI dual, and is saturated with subspaces which are HI and have HI dual. The following dichotomy theorem is proved: any infinite dimensional Banach space contains a quotient of subspace which either has an unconditional basis, or has the…

2006-03-08math.FA

Some stability properties of $c_0$-saturated spaces

A Banach space is $c_0$-saturated if all of its closed infinite dimensional subspaces contain an isomorph of $c_0$. In this article, we study the stability of this property under the formation of direct sums and tensor products. Some of the results are: (1) a slightly more general version of the fact that $c_0$-sums of $c_0$-saturated spaces are $c_0$-saturated; (2) $C(K,E)$ is $c_0$-saturated if both $C(K)$ and $E$ are; (3) the tensor product $JH\tilde{\otimes}_εJH$ is $c_0$-saturated, where $JH$ is the James Hagler space.

1993-06-21math.FA

Algebras of diagonal operators of the form scalar-plus-compact are Calkin algebras

For every Banach space $X$ with a Schauder basis consider the Banach algebra $\mathbb{R} I\oplus\mathcal{K}_\mathrm{diag}(X)$ of all diagonal operators that are of the form $λI + K$. We prove that $\mathbb{R} I\oplus\mathcal{K}_\mathrm{diag}(X)$ is a Calkin algbra i.e., there exists a Banach space $\mathcal{Y}_X$ so that the Calkin algebra of $\mathcal{Y}_X$ is isomorphic as a Banach algebra to $\mathbb{R} I\oplus\mathcal{K}_\mathrm{diag}(X)$. Among other applications of this theorem we obtain that certain hereditarily indecomposable spaces and the James spaces $J_p$ and their duals endowed wi…

2017-11-03math.FA

A $c\_0$-saturated Banach space with no long unconditional basic sequences

We present a Banach space $\mathfrak X$ with a Schauder basis of length $ω\_1$ which is saturated by copies of $c\_0$ and such that for every closed decomposition of a closed subspace $X=X\_0\oplus X\_1$, either $X\_0$ or $X\_1$ has to be separable. This can be considered as the non-separable counterpart of the notion of hereditarily indecomposable space. Indeed, the subspaces of $\mathfrak X$ have ``few operators'' in the sense that every bounded operator $T:X \to \mathfrak{X}$ from a subspace $X$ of $\mathfrak{X}$ into $\mathfrak{X}$ is the sum of a multiple of the inclusion and a $ω\_1$-sin…

2006-10-18math.FAmath.LO

更多相关论文收起更多论文

关于 $JT_*$ 空间上的显式定义范数

Explicity Defined Norms on $JT_*$ Spaces

National Technical University of Athens（雅典国立技术大学）；York University（约克大学）

构造具有显式范数的 Banach 空间 $X_\alpha$，模拟 James 树空间前对偶 $JT_*$ 的性质，其具有收缩二进基、补余 $\ell_2$-饱和性，且双对偶商等距于 $c_0(2^{\mathbb{N}})$。

2026-09-28math.FA

$F_σ$-理想、着色与Banach空间中的表示

$F_σ$-ideals, colorings, and representation in Banach spaces

本文研究$F_σ$-理想在Banach空间中的表示，利用$c$-着色理想刻画$\mathcal{B}$-与$\mathcal{C}$-理想，并构造不可在$c_0$中表示的$\mathcal{B}$-理想，揭示组合与表示的联系。

2025-01-26math.COmath.FAmath.LO