• ON b -FRAMES IN BANACH SPACES

Abstract

In the paper the generalization of the notion -frame in Banach spaces is given by means of bilinear mappings and the notion of -convergence and -representation systems are introduced. The relations between these notions are established. The criterion when the system in Banach space forms -frame, is given. The projection description of -frame is constructed. Using a linear algorithm of expansion in -frame, the extremality estimation for the coefficients of expansion in -frame are established.

Key words: -frame, expansion in -frame, -basis, -completeness , -space.

2000 Mathematics Subject Classification: 41A17, 41A58, 42C15.