On Shrinking and Boundedly Complete Schauder Frames of Banach spaces

2009/10/18 by Liu, Rui · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.0910.3369

Abstract

This paper studies Schauder frames in Banach spaces, a concept which is a natural generalization of frames in Hilbert spaces and Schauder bases in Banach spaces. The associated minimal and maximal spaces are introduced, as are shrinking and boundedly complete Schauder frames. Our main results extend the classical duality theorems on bases to the situation of Schauder frames. In particular, we will generalize James' results on shrinking and boundedly complete bases to frames. Secondly we will extend his characterization of the reflexivity of spaces with unconditional bases to spaces with unconditional frames.

Cited by

• Approximation properties and quantitative estimation for uniform ball-covering property of operator spaces

Related

• On characterizations of a some classes of Schauder frames in Banach spaces
• Upper and lower estimates for schauder frames and atomic decompositions
• Shrinking Schauder Frames and their Associated Bases
• Hilbert-Schauder Frame Operators
• Besselian Schauder Frames and the Structure of Banach Spaces