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New double inequalities for g-frames in Hilbert [Formula: see text]-modules.

Zhong-Qi Xiang1

  • 1College of Mathematics and Computer Science, Shangrao Normal University, Shangrao, 334001 People's Republic of China.

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|July 22, 2016
PubMed
Summary

This study introduces new double inequalities for g-frames in Hilbert modules, offering insights into frame theory. The findings generalize existing results, enhancing the understanding of g-frame properties.

Keywords:
Hilbert [Formula: see text]-moduleInequalityScalarg-Frame

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Area of Science:

  • Functional Analysis
  • Operator Theory
  • Hilbert Modules

Background:

  • G-frames are generalizations of frames in Hilbert spaces.
  • Hilbert modules extend the concept of Hilbert spaces.
  • Understanding frame properties is crucial in various areas of applied mathematics and signal processing.

Purpose of the Study:

  • To establish novel double inequalities for g-frames in Hilbert modules.
  • To investigate the properties of these inequalities involving specific scalar parameters.
  • To demonstrate the generalizability of the findings by recovering existing results.

Main Methods:

  • Utilizing the definitions and properties of g-frames in Hilbert modules.
  • Applying techniques from functional analysis to derive inequalities.
  • Algebraic manipulation and theoretical proofs.

Main Results:

  • Two types of double inequalities for g-frames in Hilbert modules are established.
  • The inequalities involve scalar parameters, denoted by specific formulas.
  • A key finding is that these inequalities reduce to known results when a specific parameter is set to zero.

Conclusions:

  • The established double inequalities provide a new framework for analyzing g-frames in Hilbert modules.
  • The results contribute to the advancement of frame theory and its applications.
  • The work highlights the utility of g-frames in generalizing and extending existing concepts in functional analysis.