Related papers: Multiplicative partial isometries, manageability, …

We prove that amenability of a unitary co-representation $U$ of a locally compact quantum group passes to unitary co-representations that weakly contain $U$. This generalizes a result of Bekka, and answers affirmatively a question of…

We construct uncountably many mutually nonisomorphic simple separable stably finite unital exact C$^\ast$-algebras which are not isomorphic to their opposite algebras. In particular, we prove that there are uncountably many possibilities…

Any multiplier Hopf *-algebra} with positive integrals gives rise to a locally compact quantum group (in the sense of Kustermans and Vaes). As a special case of such a situation, we have the compact quantum groups (in the sense of…

It is shown that every linear strong Birkhoff-James isomorphism between unital $C^*$-algebras is a $*$-isomorphism followed by a unitary multiplication. Moreover, as a partial extension of this result to the non-unital case, the form of…

The following topics are presented in these notes: Elements of Banach algebras, Banach algebras of the form $L^1(G)$, where $G$ is a locally compact group, spectrum of elements of Banach algebras, the spectral theory of compact operators on…

A well-known theorem of Blackadar and Handelman states that every unital stably finite C*-algebra has a bounded quasitrace. Rather strong generalizations of stable finiteness to the non-unital case can be obtained by either requiring the…

We describe the envelope C*-algebra associated to a partial action of a countable discrete group on a locally compact space as a groupoid C*-algebra (more precisely as a C*-algebra from an equivalence relation) and we use our approach to…

We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative…

We define, for a locally compact quantum group $G$ in the sense of Kustermans--Vaes, the space of $LUC(G)$ of left uniformly continuous elements in $L^\infty(G)$. This definition covers both the usual left uniformly continuous functions on…

We introduce a concept of the bounded rank (with respect to a positive constant) for unital C*-algebras as a modification of the usual real rank and present a series of conditions insuring that bounded and real ranks coincide. These…

Connectivity is a homotopy invariant property of separable C*-algebras which has three notable consequences: absence of nontrivial projections, quasidiagonality and a more geometric realization of KK-theory for nuclear C*-algebras using…

There are various statements in the physics literature about the stratification of quantum states, for example into orbits of a unitary group, and about generalized differentiable structures on it. Our aim is to clarify and make precise…

Let $(A,\Delta)$ be a locally compact quantum group and $(A_0,\Delta_0)$ a regular multiplier Hopf algebra. We show that if $(A_0,\Delta_0)$ can in some sense be imbedded in $(A,\Delta)$, then $A_0$ will inherit some of the analytic…

We extend known results about commutative $C^*$-algebras generated Toeplitz operators over the unit ball to the supermanifold setup. This is obtained by constructing commutative $C^*$-algebras of super Toeplitz operators over the super ball…

Intrinsic symmetry of the existing protocols of quantum dialogue are explored. It is shown that if we have a set of mutually orthogonal $n$-qubit states {\normalsize $\{|\phi_{0}>,|\phi_{1}>,....,|\phi_{i}<,...,|\phi_{2^{n}-1}>\}$ and a set…

Given a computably locally compact Polish space $M$, we show that its 1-point compactification $M^*$ is computably compact. Then, for a computably locally compact group $G$, we show that the Chabauty space $\mathcal S(G)$ of closed…

Starting from an abstract setting for the Lueders - von Neumann quantum measurement process and its interpretation as a probability conditionalization rule in a non-Boolean event structure, the author derived a certain generalization of…

Let $\ell$ be a length function on a group G, and let $M_{\ell}$ denote the operator of pointwise multiplication by $\ell$ on $\bell^2(G)$. Following Connes, $M_{\ell}$ can be used as a ``Dirac'' operator for $C_r^*(G)$. It defines a…

The notion of almost elementariness for a locally compact Hausdorff \'{e}tale groupoid $\mathcal{G}$ with a compact unit space was introduced by the authors as a sufficient condition ensuring the reduced groupoid $C^*$-algebra…

We find a description of the restriction of doubly stochastic maps to separable abelian $C^*$-subalgebras of a II$_1$ factor $\cM$. We use this local form of doubly stochastic maps to develop a notion of joint majorization between…