Extensions of factorial states of -algebras |
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Authors: | RJ Archbold CJK Batty |
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Institution: | Department of Mathematics, University of Aberdeen, Edward Wright Building, Dunbar Street, Aberdeen AB9 2TY, Scotland;Department of Mathematics, University of Edinburgh, King''s Buildings, Edinburgh EH9 3JZ, Scotland |
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Abstract: | Let A be a -algebra, B be a -subalgebra of A, and φ be a factorial state of B. Sometimes, φ may be extended to a factorial state of A by a tensor product method of Sakai (“-algebras and -algebras, Springer-Verlag, Berlin/Heidelberg/ New York 1971”). Sometimes, there is a weak expectation of A into , and then factorial extensions may be found by a method of Sakai and Tsui (Yokohama Math. J.29 (1981), 157–160). These two methods are shown to have the same effect, and the factorial extensions produced by them are analysed. |
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