Left Hilbert Algebras

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 125)


This chapter is devoted to the foundation of non-commutative integration theory. In the first volume of this book, we have seen the strong similarity between the theory of operator algebras and the integration theory. To explore this similarity further, it is necessary to work on the theory of left Hilbert algebras. It is the non-commutative counter part of the algebra of all bounded square integrable functions on a measure space.


Measurable Field Operator Algebra Closed Operator Polar Decomposition Graph Norm 
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Notes on Chapter VI

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© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

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