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Multiplier operator algebras and applications.

David P Blecher1, Vrej Zarikian

  • 1Department of Mathematics, University of Houston, Houston, TX 77204, USA. dblecher@math.uh.edu

Proceedings of the National Academy of Sciences of the United States of America
|January 9, 2004
PubMed
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This study explores one-sided multipliers in operator spaces, revealing their connection to latent algebraic structures. New findings and applications, particularly concerning one-sided M-ideals, are presented.

Area of Science:

  • Operator Algebras
  • Functional Analysis
  • Operator Space Theory

Background:

  • One-sided multipliers are crucial for understanding hidden algebraic properties within operator spaces.
  • Previous research has established their significance in various operator algebra applications.

Purpose of the Study:

  • To survey existing knowledge on one-sided multipliers and their applications.
  • To introduce novel results and applications of one-sided multipliers, focusing on one-sided M-ideals.

Main Methods:

  • Literature review of existing theories on operator space multipliers.
  • Development and presentation of new theoretical results concerning one-sided multipliers.
  • Exploration of new applications in the context of operator algebras and M-ideals.

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Main Results:

  • A comprehensive overview of one-sided multipliers and their established roles in operator algebras.
  • Introduction of new theorems and properties related to one-sided multipliers.
  • Demonstration of novel applications, primarily focused on one-sided M-ideals.

Conclusions:

  • One-sided multipliers offer a powerful lens for uncovering latent operator algebraic structures.
  • The study expands the theoretical framework and practical applications of one-sided multipliers, especially in relation to M-ideals.