Bessel Sequences and Frames in Semi-inner Product Spaces

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


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 \(l^{p}\), \(1<p<\infty \).


Semi-inner product space Uniformly convex smooth Banach space Bessel sequence Frame 



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


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Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Dhirubhai Ambani Institute of Information and Communication TechnologyGandhinagarIndia
  2. 2.Department of MathematicsIndian Institute of Technology KharagpurKharagpurIndia
  3. 3.Department of MathematicsUniversity of Central FloridaOrlandoUSA

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