Analysis of conditions for frame functions, examples with the orthogonal functions

Abstract

We analyse the properties of frame functions g _i , i∈ℕ₀, and spaces ˘Θ, resp., , in order to have {g _i } as a Banach frame for a Banach space X w.r.t. ˘Θ, resp., Fréchet frame for a Fréchet space w.r.t. . Examples with orthogonal functions in Hilbert spaces describes the assertions.

Keywords:

• frames
• orthogonal basis
• sequence space
• CB property

AMS Subject Classification :

• 42C15
• 44A55
• 42C05
• 46A13

Acknowledgements

This research was supported by MNZZS of Serbia, Project 144016. This research was supported by DAAD.

Notes

The numeration is as in the Arxiv version of 7.