Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 0707.0147

Tsirelson like operator spaces

Hun Hee Lee
View original source ↗Read source document ↗Export metadata ↓

Abstract

We construct nontrivial examples of weak-$C_p$ ($1\leq p \leq \infty$) operator spaces with the local operator space structure very close to $C_p = [R, C]_{\frac{1}{p}}$. These examples are non-homogeneous Hilbertian operator spaces, and their constructions are similar to that of 2-convexified Tsirelson's space by W. B. Johnson.

Explore related subjects

math.FAmath.OA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Hun Hee Lee. 2007-07-02. Tsirelson like operator spaces. https://arxiv.org/abs/0707.0147

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Products of Berezin Transforms on Generalized Fock Spaces

We study products $B_{α,m}^{(d)}B_{β,m}^{(d)}$ of Berezin transforms on generalized Fock spaces over $\mathbb C^d$. We establish a result for $m\neq2$: if $B_{α,m}^{(d)}B_{β,m}^{(d)}$ coincides with another such product, then the weight parameters of the second product must be $(α,β)$. As consequences, we characterize when two Berezin transforms commute and when the product of two Berezin transforms is again a Berezin transform.

math.FA↗
arXiv2026

Restriction of Fractional Derivatives of the Fourier Transform

We consider the differentiability of the Fourier transform of $f \in L^p(\mathbb{R}^n)$ at points on the graph of a function with non-vanishing Gaussian curvature. In particular, we show that if the values of $\widehat{f}$ along the graph possess $H^\ell$ Sobolev regularity, then this implies a certain degree of regularity of $\widehat{f}$ in the last coordinate direction as well. Two types of results are proved: One controls the $β$-order derivative in the last direction in terms of its $H^{-s}$ norm for suitable combinations of $(β, p, s, \ell)$. This extends the result in \cite{GoldStol}*{Theorem 1.12} to fractional derivatives and to some of its sharp endpoints. In particular, we recover the sharp range in the $s=0$ case where $\frac{\partial \widehat{f}}{\partial ξ_n}$ has a surface restriction in $L^2$. The second set of results is about $L^2(\mathbb{R}^n)$ bounds for difference quotients and fractional difference quotients of $\widehat{f}$, generalizing results in \cite{G2016}.

math.FA↗
arXiv2026

$J$-class weighted translations on locally compact groups

A bounded linear operator $T$ on a Banach space $X$ (not necessarily separable) is said to be $J$-class operator whenever the extended limit set, say $J_T(x)$ equals $X$ for some vector $x\in X$. Practically, the extended limit sets localize the dynamical behavior of operators. In this paper, using the extended limit sets we will examine the necessary and sufficient conditions for the weighted translation $T_{a,ω}$ to be $J$-class on a locally compact group $G$, within the setting of $ L^p$-spaces for $ 1 \leq p < \infty $. Precisely, we delineate the boundary between $J$-class and hypercyclic behavior for weighted translations. Then, we will show that for the torsion elements in locally compact groups, unlike the case of non-dense orbits of weighted translations, we have $J_{T_{a,ω}}(0)=L^p(G)$. Finally, we will provide some examples on which the weighted translation $ T_{a,ω}$ is $J$-class but it fails to be hypercyclic.

math.FA↗