Research On Finite Operator-Valued Frames And Modular Frames

In this paper, we study finite operator-valued frames on Hilbert spaces and finite modular framesin finite generated Hilbert C^*modules.The main results obtained in this paper are listed as follows:（1） We show that every operator-valued frame on a Hilbert space either can be written as notonly, a sum of three orthonormal operator valued frames but also, a linear combination of anorthonormal operator valued frame and a Riesz operator valued frame;（2） Let {V j}j{V_j}_j∈J Jbe a operator-valued frame on a Hilbert space H, and R be a subset of J. Anecessary and sufficient condition determined by the subset R such that {V j}j{V_j}_j∈J Rcis still anoperator-valued frame for H is given;（3） We study the similarity and duality for finite operator-valued frame. Also, it is shown that theequal-norm Parseval operator-valued frames are optimal in the case that one packet of data is lost insignal transmission;（4） We study frames potential of modular frames for finite generated Hilbert C^*modules.