Upper and lower estimates for Schauder frames and atomic decompositions

• Autorzy: Kevin Beanland , Daniel Freeman , Rui Liu
• Języki publikacji: EN

Abstrakty

EN

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 infinite-dimensional Banach space has a Schauder frame, then it also has a Schauder frame which is not shrinking.

Kategorie tematyczne

• 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 231
• Numer: 2
• Strony: 161-188

Daty

wydano

2015

Twórcy

autor

Kevin Beanland

• Washington and Lee University, 204 W. Washington St., Lexington, VA 24450, U.S.A.

autor

Daniel Freeman

• Department of Mathematics, and Computer Science, Saint Louis University, St. Louis, MO 63103, U.S.A.

autor

Rui Liu

• Department of Mathematics and LPMC, Nankai University, Tianjin 300071, P.R. China
• Department of Mathematics, Texas A&M University, College Station, TX 77843, U.S.A.

Identyfikatory

DOI

10.4064/fm231-2-4