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SUMS OF C-FRAMES , C-RIESZ BASES AND ORTHONORMAL MAPPINGS

In this paper we introduce and prove some new concepts and results on c-frames for Hilbert spaces. We define c-Riesz bases for a Hilbert space H and state some results to characterize them. Then, we give necessary and sufficient conditions on c-Bessel mappings f and g and operators L1, L2 on H so that L1f+ L2g is a c-frame for H. This allows us to construct a large number of new cframes by existing c-frames. Also, we define orthonormal mappings for H and we specify a necessary and sufficient condition to represent a c-frame as a linear combination of two orthonormal mappings. Moreover, we show that every c-frame can be written as a (multiple of a) sum of two Parseval c-frames; it can also be written as a (multiple of a) sum of an orthonormal mapping and a c-Riesz basis.