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The classical bounded symmetric domains

Chapter
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Part of the Progress in Mathematical Physics book series (PMP, volume 40)

Abstract

The definition of bounded symmetric domains is geometric in nature and does not seem, at first glance, to be connected to the category of operators on Hilbert spaces. Nevertheless, we have already seen in the previous chapter that the spin factor has certain properties found in operator spaces, such as spectral decomposition, representation by Pauli matrices, and Peirce decomposition. Surprisingly, most BSDs are unit balls of operator spaces. Such domains are calledclassical domains.They provide a familiar setting in which to introduce some of the more abstract concepts connected with BSDs.

Keywords

Hilbert Space Unit Ball Polar Decomposition Triple Product Symmetric Domain 
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 New York 2005

Authors and Affiliations

  1. 1.Department of MathematicsJerusalem College of TechnologyJerusalemIsrael
  2. 2.Department of MathematicsJerusalem College of TechnologyJerusalemIsrael

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