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Some Identities and Inequalities for Hilbert–Schmidt Frames

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Abstract

In this paper, we establish Parseval type identities and surprising new inequalities for Hilbert–Schmidt frames. Our results generalize and improve the remarkable results which have been obtained by Balan et al. and Găvruţa.

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Acknowledgements

The author is deeply indebted to Prof. Radu Balan for several valuable suggestions concerning Theorems 3.5 and 3.11. The author also wishes to thank Dr. J. Swain for several fruitful discussions. The author is grateful to the Ministry of Human Resource Development, India for providing the research fellowship and Indian Institute of Technology Guwahati, India for the support provided during the period of this work. Further, the author thanks the anonymous referee for valuable suggestions which helped to improve the paper.

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  1. Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, 781039, India

    Anirudha Poria

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  1. Anirudha Poria
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Poria, A. Some Identities and Inequalities for Hilbert–Schmidt Frames. Mediterr. J. Math. 14, 59 (2017). https://doi.org/10.1007/s00009-017-0866-1

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