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Starting with a $W^{*}$-algebra $M$ we use the inverse system obtained by cutting down $M$ by its (central) projections to define an inverse limit of $W^{*}$-algebras, and show that how this pro-$W^{*}$-algebra encodes the local structure…
Let $H$ be a separable Hilbert space with a fixed orthonormal basis. Let $\mathbb B^{(k)}(H)$ denote the set of operators, whose matrices have no more than $k$ non-zero entries in each line and in each column. The closure of the union (over…
On a separable C*-algebra A every (completely) bounded map, which preserves closed two sided ideals, can be approximated uniformly by elementary operators if and only if A is a finite direct sum of C*-algebras of continuous sections…
In this paper we consider the unbounded local completely positive and local completely contractive maps on maximal tensor product of unital locally C*-algebras and discuss on extremal points of certain convex subsets in the set of such…
All operator algebras have (not necessarily irreducible) boundary representations. A unital operator algebra has enough such boundary representations to generate its C*-envelope.
We consider various quotients of the C*-algebra of bounded operators on a nonseparable Hilbert space, and prove in some cases that, consistently, there are many outer automorphisms.
The operator space generated by peripheral eigenvectors of a unital normal completely positive map $P$ on a von Neumann algebra has a C*-algebra structure. This C*-algebra is known as the \textit{peripheral Poisson boundary} of $P$. For a…
In this paper we study the completely bounded anti-isomorphisms on operator algebras, that work similarly to the involutions with the exception for the property of being completely isometric. We elaborate the Blecher's characterization…
We consider a version of a famous open problem formulated by Kadison, asking whether bounded representations of operator algebras are automatically completely bounded. We investigate this question in the context of amenable operator…
In this paper, we construct, for a certain class of semigroup dynamical systems, two operator algebras that are universal with respect to their corresponding covariance conditions: one being self-adjoint, and another being non-self-adjoint.…
We construct an example of a Hilbert C*-module which shows that Troitsky's theorem on the geometrical essence of A-compact operators between Hilbert C*-modules is not extendable to a not countably generated module case (even in the case of…
We establish a description of the maximal C*-algebra of quotients of a unital C*-algebra $A$ as a direct limit of spaces of completely bounded bimodule homomorphisms from certain operator submodules of the Haagerup tensor product…
We continue our study of the general theory of possibly nonselfadjoint algebras of operators on a Hilbert space, and modules over such algebras, developing a little more technology to connect `nonselfadjoint operator algebra' with the…
It is shown that the operator space generated by peripheral eigenvectors of a unital completely positive map on a von Neumann algebra has a $C^*$-algebra structure. This extends the notion of non-commutative Poisson boundary by including…
We compute the C*-algebra generated by a group of composition operators acting on certain reproducing kernel Hilbert spaces over the disk, where the symbols belong to a non-elementary Fuchsian group. We show that such a C*-algebra contains…
Let $C^*(\cls)$ be the $C^*$ algebra generated by an operator system $\cls$ i.e. a unital $*$-closed subspace of a unital $C^*$ algebra $\cla$. We prove that any complete order isomorphism $\cli:\cls \raro \cls'$ between two such operator…
In this paper, we provide a representation of a certain class of C*-valued positive sesquilinear and linear maps on non-unital quasi *-algebras. Also, we illustrate our results on the concrete examples of non-unital Banach quasi *-algebras,…
We combine the notion of norming algebra introduced by Pop, Sinclair and Smith with a result of Pisier to show that if A_1 and A_2 are operator algebras, then any bounded epimorphism of A_1 onto A_2 is completely bounded provided that A_2…
We give a structural characterisation of linear operators from one $C^\ast$% -algebra into another whose adjoints map extreme points of the dual ball onto extreme points. We show that up to a $\ast$-isomorphism, such a map admits of a…
We prove that the tensor algebra of a C*-correspondence $X$ is Dirichlet if and only if $X$ is a Hilbert bimodule. As a consequence, we point out and fix an error appearing in the proof of a famous result of Duncan. Secondly we answer a…