The Characterization and Stability of g-Riesz Frames for Super Hilbert Space

Abstract

G-frames and g-Riesz frames as generalized frames in Hilbert spaces have been studied by many authors in recent years. The super Hilbert space has a certain advantage compared with the Hilbert space in the field of studying quantum mechanics. In this paper, for super Hilbert spaceH⊕K, the definitions of a g-Riesz frame and minimal g-complete are put forward; also a characterization of g-Riesz frames is obtained. In particular, we generalize them to general super Hilbert spaceL1⊕L2⊕⋯⊕Ln. Finally, a conclusion of the stability of a g-Riesz frame for the super Hilbert space is given.