Rocky Mountain Journal of Mathematics

Tensor products of unbounded operator algebras

M. Fragoulopoulou, A. Inoue, and M. Weigt

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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.

Article information

Rocky Mountain J. Math., Volume 44, Number 3 (2014), 895-912.

First available in Project Euclid: 28 September 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46M05: Tensor products [See also 46A32, 46B28, 47A80] 47L60: Algebras of unbounded operators; partial algebras of operators

$O^*$-algebra $EW^*$-algebra $GW^*$-algebra $W^*$-tensor product $GW^*$-tensor product properly $W^*$-infinite $GW^*$-algebra


Fragoulopoulou, M.; Inoue, A.; Weigt, M. Tensor products of unbounded operator algebras. Rocky Mountain J. Math. 44 (2014), no. 3, 895--912. doi:10.1216/RMJ-2014-44-3-895.

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