On O*-Representability and C*-Representability of ∗-algebras.
نویسنده
چکیده
Characterization of the *-subalgebras 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.
منابع مشابه
Undecidable Problems on Representability as Binary Relations
We establish the undecidability of representability and of finite representability as algebras of binary relations in a wide range of signatures. In particular, representability and finite representability are undecidable for Boolean monoids and lattice ordered monoids, while representability is undecidable for Jónsson’s relation algebra. We also establish a number of undecidability results for...
متن کاملOn Unitary Representability of Topological Groups
We prove that the additive group (E∗, τk(E)) of an L∞-Banach space E, with the topology τk(E) of uniform convergence on compact subsets of E, is topologically isomorphic to a subgroup of the unitary group of some Hilbert space (is unitarily representable). This is the same as proving that the topological group (E∗, τk(E)) is uniformly homeomorphic to a subset of ` κ 2 for some κ. As an immediat...
متن کاملNumerical Representability of Ordered Topological Spaces with Compatible Algebraic Structure
We analyze the numerical representability of total preorders defined on semitopological real algebras through continuous order-preserving real-valued functions that are also additive and multiplicative. The results obtained are used to interpret important concepts arising in Social Choice theory.
متن کاملComplementation in Representable Theories of Region-Based Space
Through contact algebras we study theories of mereotopology in a uniform way that clearly separates mereological from topological concepts. We identify and axiomatize an important subclass of closure mereotopologies (CMT) called unique closure mereotopologies (UCMT) whose models always have orthocomplemented contact algebras (OCA) an algebraic counterpart. The notion of MT-representability, a w...
متن کاملPartial Recursive Functions and Finality
We seek universal categorical conditions ensuring the representability of all partial recursive functions. In the category Pfn of sets and partial functions, the natural numbers provide both an initial algebra and a final coalgebra for the functor 1 + −. We recount how finality yields closure of the partial functions on natural numbers under Kleene’s μ-recursion scheme. Noting that Pfn is not c...
متن کامل