Perturbations and New Characterizations of Woven P-Frames

Abstract

In this paper, we prove several functional-analytic properties of weaving p-frames. We first prove that Banach woven p-frames are stable under small perturbations. This is inspired by corresponding classical perturbation results for bases. We introduce new and weaker conditions that ensure the desired stability. We then present several approaches for identifying and constructing of woven p-frames. To this end, we present some conditions under which a p-frame and a finite family of operators constitute a woven p-frame.

Key words and phrases. Weaving p-frames, weaving p-Riesz bases, perturbations.

2000 Mathematics Subject Classification. Primary: 46B15; 46B20 Secondary: 42C15