(p, Y )-Operator frames for a Banach space ✩

In this paper, (p, Y )-Bessel operator sequences, operator frames and (p, Y )-Riesz bases for a Banach space X are introduced and discussed as generalizations of the usual concepts for a Hilbert space and of the g-frames. It is proved that the set Bp X (Y ) of all (p, Y )-Bessel operator sequences for a Banach space X is a Banach space and isometrically isomorphic to the operator space B(X, p (Y )). Some necessary and sufficient conditions for a sequence of operators to be a (p, Y )-Bessel operator sequence are given. Also, a characterization of an independent (p, Y )-operator frame for X is obtained. Lastly, it is shown that an independent (p, Y )-operator frame for X is just a (p, Y )-Riesz basis for X and has a unique dual (q, Y ∗)-operator frame for X∗.