Decompositions of Operator Algebras, 1 and 2.

Intro -- DECOMPOSITIONS OF OPERATOR ALGEBRAS. I -- 1. Introduction -- 2. Definitions and notations -- 3. Decomposition of &amp -- state relative to ia commutative algebra -- 4. Direct integrals of Hilbert spaces -- 5. Maximal decompositions -- 6. Decomposition of a W*-algebra into factors -- 7. Decomposition of a group representation into irreducible representations -- 8. Decomposition of an invariant measure Into ergodic parts -- 9. The Fourier transform for separable unimodular groups -- 10. Deflation of decompositions -- References -- DECOMPOSITIONS OF OPERATOR ALGEBRAS. II -- 1. Introduction -- PART II. COMMUTATIVE ALGEBRAS -- 2. Definitions and technical preliminaries -- 3. Structure of maximal abelian W*-algebras -- 4. Structure of commutative W*-algebras -- 5. Unitary invariants of commutative W-ft-algebras and of SA operators -- 6. Applications -- PART II. NON-COMMUTATIVE ALGEBRAS -- 7. Decomposition theory -- 8. Algebras of uniform multiplicity -- 9. Algebras of type I -- References.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.