相关论文: Matrix Ordered Operator Algebras

We associate to any Riemannian symmetric space (of finite or infinite dimension) a L$^*$-algebra, under the assumption that the curvature operator has a fixed sign. L$^*$-algebras are Lie algebras with a pleasant Hilbert space structure.…

Order unit property of a positive element in a $C^{*}$-algebra is defined. It is proved that precisely projections satisfy this order theoretic property. This way, unital hereditary $C^{*}$-subalgebras of a $C^{*}$-algebra are…

The generalized state space of a commutative C*-algebra, denoted S_H(C(X)), is the set of positive unital maps from C(X) to the algebra B(H) of bounded linear operators on a Hilbert space H. C*-convexity is one of several non-commutative…

In the present paper we study the structure of C^*-algebras generated by the components of the polar decompositions of operators in Hilbert space satisfying certain commutation relations.

In this paper we study the structure of the $C^*$-algebra, generated by the representation of the paths semigroup on a partially ordered set (poset) and get the net of isomorphic $C^*$-algebras over this poset. We construct the extensions…

Given a group G, we construct, in a canonical way, an inverse semigroup S(G) associated to G. The actions of S(G) are shown to be in one-to-one correspondence with the partial actions of G, both in the case of actions on a set, and that of…

Jordan operator algebras are norm-closed spaces of operators on a Hilbert space with $a^2 \in A$ for all $a \in A$. We study noncommutative topology, noncommutative peak sets and peak interpolation, and hereditary subalgebras of Jordan…

Certain $*$-semigroups are associated with the universal $C^*$-algebra generated by a partial isometry, which is itself the universal $C^*$-algebra of a $*$-semigroup. A fundamental role for a $*$-structure on a semigroup is emphasized, and…

In the present article we review an approximation procedure for amenable traces on unital and separable C*-algebras acting on a Hilbert space in terms of F\o lner sequences of non-zero finite rank projections. We apply this method to…

We examine the properties of algebras of linear transformations that leave invariant all subspaces in a totally ordered lattice of subspaces of an arbitrary vector space. We compare our results with those that apply for the corresponding…

The weak operator topology closed operator algebra on $L^2(R)$ generated by the one-parameter semigroups for translation, dilation and multiplication by $exp(i\lambda x), \lambda \geq 0$, is shown to be a reflexive operator algebra, in the…

We describe the C*-algebras of the Heisenberg group H_n, n\geq 1, and the thread-like Lie group G_N, N\geq 3, in terms of C*-algebras of operator fields.

Let $X$ be an operator space, let $\phi$ be a product on $X$, and let $(X,\phi)$ denote the algebra that one obtains. We give necessary and sufficient conditions on the bilinear mapping $\phi$ for the algebra $(X,\phi)$ to have a completely…

It is known that the classical Hilbert--Schmidt theorem can be generalized to the case of compact operators in Hilbert $A$-modules $H_A^*$ over a $W^*$-algebra of finite type, i.e. compact operators in $H_A^*$ under slight restrictions can…

This is a sequel to our paper on nonlinear completely positive maps and dilation theory for real involutive algebras, where we have reduced all representation classification problems to the passage from a $C^*$-algebra ${\mathcal A}$ to its…

Let H be a complex Hilbert space of dimension no less than 2 and B(H) be the algebra of all bounded linear operators on H. We give the form of surjective maps on B(H) preserving c-numerical range of operator products when the maps satisfy…

In this article we survey some of the recent goings-on in the classification programme of C$^*$-algebras, following the interesting link found between the Cuntz semigroup and the classical Elliott invariant and the fact that the Elliott…

In this article we give a short and informal overview of some aspects of the theory of C*- and von Neumann algebras. We also mention some classical results and applications of these families of operator algebras.

The purpose of the present paper is to lay the foundations for a systematic study of tensor products of operator systems. After giving an axiomatic definition of tensor products in this category, we examine in detail several particular…

Jordan operator algebras are norm-closed spaces of operators on a Hilbert space with a^2 in A for all a in A. In two recent papers by the authors and Neal, a theory for these spaces was developed. It was shown there that much of the theory…