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Bessel Sequences and Frames in Semi-inner Product Spaces

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Mathematics and Computing (ICMC 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 655))

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Abstract

In this paper, the concept of Bessel sequence and frame are introduced in semi-inner product spaces. Some properties of the Bessel sequences and frame are investigated in smooth uniformly convex Banach spaces. One characterization of the space of all Bessel sequences has been pointed out. Examples of frames are constructed in the real sequence spaces \(l^{p}\), \(1<p<\infty \).

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Acknowledgements

The authors are thankful to the referees for their valuable suggestions which improved the presentation of the paper.

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Authors and Affiliations

  1. Dhirubhai Ambani Institute of Information and Communication Technology, Gandhinagar, 382007, India

    N. K. Sahu

  2. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721302, India

    C. Nahak

  3. Department of Mathematics, University of Central Florida, Orlando, FL, 32816, USA

    Ram N. Mohapatra

Authors
  1. N. K. Sahu
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  2. C. Nahak
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  3. Ram N. Mohapatra
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Corresponding author

Correspondence to N. K. Sahu .

Editor information

Editors and Affiliations

  1. Haldia Institute of Technology, Haldia, India

    Debasis Giri

  2. University of Central Florida, Orlando, Florida, USA

    Ram N. Mohapatra

  3. Freie Universität Berlin, Berlin, Germany

    Heinrich Begehr

  4. Fordham University, Bronx, New York, USA

    Mohammad S. Obaidat

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Sahu, N.K., Nahak, C., Mohapatra, R.N. (2017). Bessel Sequences and Frames in Semi-inner Product Spaces. In: Giri, D., Mohapatra, R., Begehr, H., Obaidat, M. (eds) Mathematics and Computing. ICMC 2017. Communications in Computer and Information Science, vol 655. Springer, Singapore. https://doi.org/10.1007/978-981-10-4642-1_14

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  • DOI: https://doi.org/10.1007/978-981-10-4642-1_14

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-4641-4

  • Online ISBN: 978-981-10-4642-1

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