Currently displaying 1 – 2 of 2

Showing per page

Order by Relevance | Title | Year of publication

Generalized-lush spaces and the Mazur-Ulam property

Dongni Tan;  Xujian Huang;  Rui Liu — 2013

Studia Mathematica

We introduce a new class of Banach spaces, called generalized-lush spaces (GL-spaces for short), which contains almost-CL-spaces, separable lush spaces (in particular, separable C-rich subspaces of C(K)), and even the two-dimensional space with hexagonal norm. We find that the space C(K,E) of vector-valued continuous functions is a GL-space whenever E is, and show that the set of GL-spaces is stable under c₀-, l₁- and l ∞ -sums. As an application, we prove that the Mazur-Ulam property holds for a larger...

Upper and lower estimates for Schauder frames and atomic decompositions

Kevin Beanland;  Daniel Freeman;  Rui Liu — 2015

Fundamenta Mathematicae

We prove that a Schauder frame for any separable Banach space is shrinking if and only if it has an associated space with a shrinking basis, and that a Schauder frame for any separable Banach space is shrinking and boundedly complete if and only if it has a reflexive associated space. To obtain these results, we prove that the upper and lower estimate theorems for finite-dimensional decompositions of Banach spaces can be extended and modified to Schauder frames. We show as well that if a separable...

Page 1

Download Results (CSV)