Related papers: Extensions of operator algebras I

We characterize exotic C*-algebras of twisted, principal \'etale groupoids, together with the abelian subalgebra associated to the unit space, as precisely being the inclusions "$A\subseteq B$" of C*-algebras in which $A$ is abelian,…

We introduce a method to define $C^*$-algebras from $C^*$-correspondences. Our construction generalizes Cuntz-Pimsner algebras, crossed products by Hilbert $C^*$-modules, and graph algebras.

In this paper, extensions of nonunitary rational Virasoro vertex operator algebras corresponding to some exceptional modular invariants are constructed. The uniqueness of these extensions is also established.

We give an overview of some recent developments in semigroup C*-algebras.

We consider some special type extensions of an arbitrary Lie algebra, which we call universal extensions. We show that these extensions are in one-to-one correspondence with finite dimensional associative commutative algebras. We also…

After briefly reviewing the methods that allow us to derive consistently new Lie (super)algebras from given ones, we consider enlarged superspaces and superalgebras, their relevance and some possible applications.

In this paper, we investigate the relative operator entropies in the more general settings of C*-algebras, real C*-algebras and JC-algebras. We show that all the operator inequalities on relative operator entropies still hold in these…

We survey the use of extra-set-theoretic hypotheses, mainly the continuum hypothesis, in the C*-algebra literature. The Calkin algebra emerges as a basic object of interest.

We consider the deconstruction/reconstruction of extensions in varieties of algebras which are modules expanded by multilinear operators. The parametrization of extensions determined by abelian ideals with unary actions agrees with the…

We obtain partial affirmative answers to the question whether isomorphism of the unitary groups of two C*-algebras, either as topological groups or as discrete groups, implies isomorphism of the C*-algebras as real C*-algebras.

The extension problem asks whether positive semi-definite functions on a symmetric unital subset of a discrete group can be extended to positive semi-definite functions on the whole group. It has been known at least since the work of Rudin…

We consider operators on $L^2$ spaces that expand the support of vectors in a manner controlled by some constraint function. The primary objects of study are $\mathrm C^*$-algebras that arise from suitable families of constraints, which we…

We provide a complete description of the order isomorphisms between the self-adjoint parts of $C^*$-algebras. Furthermore, we characterize such isomorphisms between general operator intervals in $AW^*$-algebras. For the description, we use…

Various questions on Lie ideals of C*-algebras are investigated. They fall roughly under the following topics: relation of Lie ideals to closed two-sided ideals; Lie ideals spanned by special classes of elements such as commutators,…

We study the ideal structure of $C^*$-algebras arising from $C^*$-correspondences. We prove that gauge-invariant ideals of our $C^*$-algebras are parameterized by certain pairs of ideals of original $C^*$-algebras. We show that our…

The study of operator algebras on Hilbert spaces, and C*-algebras in particular, is one of the most active areas within Functional Analysis. A natural generalization of these is to replace Hilbert spaces (which are $L^2$-spaces) with…

We define an ultragraph, which is a generalization of a directed graph, and describe how to associate a C*-algebra to it. We show that the class of ultragraph algebras contains the C*-algebras of graphs as well as the Exel-Laca algebras. We…

We study the concept of extended derivations of algebras which expands diverse definitions of generalized derivations given in the literature. We concentrate on the family of the anti-commutative algebras and classify such spaces of…

We will investigate the norm closure of the unitary and similarity orbits of normal operators in unital, simple, purely infinite C*-algebras. An operator theoretic proof will be given to the classification of when two normal operators are…

We transfer the theory of slack operators and sums-of-squares-criteria for lifts from convex cones to operator systems. These allow to study the following question, among others: Given an abstract operator system, is its enveloping…