TENSOR PRODUCTS OF UNBOUNDED OPERATOR ALGEBRAS

The term GW*-algebra means a generalized W*-algebra and corresponds to an unbounded generalization of a standard von Neumann algebra. It was introduced by the second named author in 1978 for developing the Tomita-Takesaki theory in algebras of unbounded operators. In this note we consider tensor pro...

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Bibliographic Details
Published in:The Rocky Mountain journal of mathematics 2014-01, Vol.44 (3), p.895-912
Main Authors: FRAGOULOPOULOU, M., INOUE, A., WEIGT, M.
Format: Article
Language:English
Subjects:
46M05
47L60
EW^-algebra
GW^-algebra
GW^-tensor product
O^-algebra
properly W^-infinite GW^-algebra
W^-tensor product
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Summary:The term GW*-algebra means a generalized W*-algebra and corresponds to an unbounded generalization of a standard von Neumann algebra. It was introduced by the second named author in 1978 for developing the Tomita-Takesaki theory in algebras of unbounded operators. In this note we consider tensor products of unbounded operator algebras resulting in a GW*-algebra. Existence and uniqueness of the GW*-tensor product is encountered, while "properly W*-infinite" GW*-algebras are introduced and their structure is investigated.
ISSN:0035-7596
1945-3795
DOI:10.1216/rmj-2014-44-3-895