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Positivity pp 27-71 | Cite as

Positivity in Operator Algebras and Operator Spaces

  • David P. Blecher
Part of the Trends in Mathematics book series (TM)

Abstract

This article is aimed at a general reader familiar with the basics of functional analysis. It begins with a quick summary of the most basic ‘facts of life’ of positivity for Hilbert space operators, or for algebras of operators on a Hilbert space. It being impossible to adequately survey the fundamental role of positivity in the field of operator algebras, since this is so extensive and ubiquitous, in the present article we review selectively some of the general principles in the subject, and give some examples of how positivity plays a central role in the field, even in settings where positivity is not at first in evidence. The topics become more progressively more specialized towards our own current interests, ending with some very recent work of ours and of others.

Keywords

Operator Space Operator Algebra Boundary Representation Approximate Identity Complete Positivity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Birkhäuser Verlag AG2007 2007

Authors and Affiliations

  • David P. Blecher
    • 1
  1. 1.Department of MathematicsUniversity of HoustonHoustonUSA

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