An appropriate representation space for controlled G-frames

2019/05/22 by Maryam Forughi, Elnaz Osgooei, Forughi, Maryam +5
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1905.08962

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arxiv created 2019/05/22 · arxiv updated 2019/05/23

Abstract

In this paper, motivating the range of operators, we propose an appropriate representation space to introduce synthesis and analysis operators of controlled g-frames and discuss the properties of these operators. Especially, we show that the operator obtained by the composition of the synthesis and analysis operators of two controlled g-Bessel sequence is a trace class operator. Also, we define the canonical controlled g-dual and show that this dual gives rise to expand coefficients with the minimal norm. Finally, we extend some known equality and inequalities for controlled g-frames.

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