Abstract
In this paper, we introduce the concept of a g-Besselian frame in a Hilbert space and discuss the relations between a g-Besselian frame and a Besselian frame. We also give some characterizations of g-Besselian frames. In the end of this paper, we discuss the stability of g-Besselian frames. Our results show that the relations and the characterizations between a g-Besselian frame and a Besselian frame are different from the corresponding results of g-frames and frames.
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Supported by Natural Science Foundation of Fujian Province, China (Grant Nos. 2009J01007, 2008J0183), the Education Commission Foundation of Fujian Province, China (Grant No. JA08013) and the Science Foundation for the Youth Scholars of Fujian Agriculture and Forestry University, China (Grant No. 07B23)
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Ding, M.L., Zhu, Y.C. g-Besselian frames in Hilbert spaces. Acta. Math. Sin.-English Ser. 26, 2117–2130 (2010). https://doi.org/10.1007/s10114-010-9081-8
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DOI: https://doi.org/10.1007/s10114-010-9081-8