Formula omitted]-Operator frames for a Banach space

Abstract

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 B X p ( 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 , ℓ 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 ∗ .