SOME RESULTS ON CONTROLLED FRAMES IN HILBERT SPACES

doi:10.1016/S0252-9602(16)30029-7

Abstract

Abstract:

We use two appropriate bounded invertible operators to define a controlled frame with optimal frame bounds. We characterize those operators that produces Parseval controlled frames also we state a way to construct nearly Parseval controlled frames. We introduce a new perturbation of controlled frames to obtain new frames from a given one. Also we reduce the distance of frames by appropriate operators and produce nearly dual frames from two given frames which are not dual frames for each other.

Key words: frames, Parseval frames, dual frames, controlled frames, reconstruction formula, perturbation

CLC Number:

94A12

Kamran MUSAZADEH, Hassan KHANDANI. SOME RESULTS ON CONTROLLED FRAMES IN HILBERT SPACES[J].Acta mathematica scientia,Series B, 2016, 36(3): 655-665.

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