Journal of Mathematical Sciences

, Volume 159, Issue 5, pp 600–652 | Cite as

Projective modules in classical and quantum functional analysis

  • A. Ya. Helemskii
Article
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Abstract

Along with the classical version, there are two “quantized” versions of the theory of operator algebras. In these lectures, the fundamental homological notion of a projective module is described in the framework of these three theories. Our initial definitions of projectivity do not go far from their prototypes in abstract algebra; however, the principal results concern essentially functional-analytic objects and, as a rule, have no purely algebraic analogs.

Keywords

Banach Space Operator Algebra Banach Algebra Homological Theory Elementary Tensor 
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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Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  • A. Ya. Helemskii
    • 1
  1. 1.Faculty of Mechanics and MathematicsMoscow State UniversityMoscowRussia

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