Topic

# O*-algebra

About: O*-algebra is a(n) research topic. Over the lifetime, 2 publication(s) have been published within this topic receiving 18 citation(s).

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TL;DR: In this paper, sufficient conditions for the existence of a faithful representation in pre-Hilbert space of a *-algebra in terms of its Groebner basis are given.

Abstract: Characterization of the *-algebras in the algebra of bounded operators acting on Hilbert space is presented. Sufficient conditions for the existence of a faithful representation in pre-Hilbert space of a *-algebra in terms of its Groebner basis are given. These conditions are generalization of the unshrinkability of monomial *-algebras introduced by C. Lance and P. Tapper. The applications to *- doubles, monomial *-algebras and several other classes of *-algebras are presented.

11 citations

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TL;DR: In this article, a tensor product of unbounded operator algebras resulting in a $GW^*$-algebra is considered, and the existence and uniqueness of the tensor products are investigated.

Abstract: 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.

7 citations