Hilbert空间中的g-Besselian框架和拟g-Riesz基

Abstract

Abstract:

g-frames, as the generalized frames, have many properties similar to those of the frames in Hilbert spaces, but not all the properties are similar. For example, Besselian frames are equivalent to near Riesz bases, but g-Besselian frames are not equivalent to near g-Riesz bases. In this paper, we give an equivalent relation between a g-Besselian frame and a near g-Riesz basis under some conditions, and also have some results on the duality of g-Besselian frames and near g-Riesz bases. Moreover, we discuss the stability of g-Besselian frames and near g-Riesz bases respectively in Hilbert spaces.

Key words: g-frame, g-Besselian frame, Near g-Riesz basis, Canonical dual g-frame, Stability

CLC Number:

42C99

DING Ming-Ling, ZHU Yu-Can, XIAO Xiang-Chun, WEN Yong-Xian. g-Besselian Frames and Near g-Riesz Bases in Hilbert Spaces[J].Acta mathematica scientia,Series A, 2014, 34(4): 948-959.

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g-Besselian Frames and Near g-Riesz Bases in Hilbert Spaces

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