New identity on Parseval p-approximate Schauder frames and applications

Abstract

A very useful identity for Parseval frames for Hilbert spaces was obtained by Balan, Casazza, Edidin, and Kutyniok. In this paper, we obtain a similar identity for Parseval p-approximate Schauder frames for Banach spaces which admits a homogeneous semi-inner product in the sense of Lumer-Giles.

Subject Classification: (2010):

• 42C15
• 46B25
• 46C50

Keywords:

• Frame
• Frame identity
• Approximate Schauder frame