مشخصات پژوهش

Let X be a refexive separable Banach space, and let pB the set of p-Bessel sequences in X^* for X. We show that pB is a non-commutative unital Banach algebra isometrically isomorphic to B(X). Also, we classify p-Bessel sequences for X in terms of different kind of operators in B(X) and B(X), and we give important characterizations of p-frames and q-Riesz sequences. Using an isomorphism between the sets pB and B(X) we obtain interesting results for p-frames in Banach spaces. Using operator theory tools, we investigate the geometry of p-Bessel sequences. Also, we show that the set of all q-Riesz bases for X^* is a topological group.