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 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. Copyright © 2014 Rocky Mountain Mathematics Consortium.