Left Hilbert Algebras
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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.
KeywordsMeasurable Field Operator Algebra Closed Operator Polar Decomposition Graph Norm
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Notes on Chapter VI
- M. Tornita, Spectral theory of operator algebras. I, Math. J. Okayama Univ., 9 (1959), 63–98. II, ibid., 10 (1960), 19–60.Google Scholar