About: O*-algebra is a(n) research topic. Over the lifetime, 2 publication(s) have been published within this topic receiving 18 citation(s).
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.
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.
Related Topics (5)
7.6K papers, 167.8K citations
5.7K papers, 76.7K citations
Chain (algebraic topology)
6.2K papers, 68.2K citations
2.7K papers, 44.3K citations
972 papers, 38.5K citations