Related papers: (No) Wigner Theorem for C*-algebras

Let $H$ be a complex Hilbert space whose dimension is not less than $3$ and let ${\mathcal F}_{s}(H)$ be the real vector space formed by all self-adjoint operators of finite rank on $H$. For every non-zero natural $k<\dim H$ we denote by…

We present a uniqueness theorem for k-graph C*-algebras that requires neither an aperiodicity nor a gauge invariance assumption. Specifically, we prove that for the injectivity of a representation of a k-graph C*-algebra, it is sufficient…

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…

Let $\mathcal{H}$ be an infinite dimensional Hilbert space and $\mathcal{B}(\mathcal{H})$ be the C*-algebra of all bounded linear operators on $\mathcal{H}$, equipped with the operator-norm. By improving the Brown-Pearcy construction,…

Suppose a C*-algebra A acts by adjointable operators on a Hilbert A-module X. Pimsner constructed a C*-algebra O_X which includes, for particular choices of X, crossed products of A by Z, the Cuntz algebras O_n, and the Cuntz-Krieger…

We study the theory of a Hilbert space H as a module for a unital C*-algebra A from the point of view of continuous logic. We give an explicit axiomatization for this theory and describe the structure of all the representations which are…

We say that a C*-algebra is nowhere scattered if none of its quotients contains a minimal open projection. We characterize this property in various ways, by topological properties of the spectrum, by divisibility properties in the Cuntz…

We consider projectivity and injectivity of Hilbert C*-modules in the categories of Hilbert C*-(bi-)modules over a fixed C*-algebra of coefficients (and another fixed C*-algebra represented as bounded module operators) and bounded…

It is shown that a C*-algebra generated by any faithful covariant representation of a Hilbert bimodule X is canonically isomorphic to the crossed product associated to X provided that Rieffel's induced representation functor X-ind is…

In a recent paper of the first author and Kashyap, a new class of modules over dual operator algebras is introduced. These generalize the W*-modules (that is, Hilbert C*-modules over a von Neumann algebra which satisfy an analogue of the…

In recent years, the traditional notion of symmetry in quantum theory was expanded to so-called generalised or categorical symmetries, which, unlike ordinary group symmetries, may be non-invertible. This appears to be at odds with Wigner's…

Let H be a full Hilbert bimodule over a C*-algebra A. We show that the Cuntz-Pimsner C*-algebra associated to H is exact if and only if A is exact. Using this result, we give alternative proofs for exactness of reduced amalgamated free…

We show that, on a Hilbert space of odd dimension, the only pure states to possess a non-negative Wigner function are stabilizer states. The Clifford group is identified as the set of unitary operations which preserve positivity. The result…

Let $\gamma = (\gamma_1,...,\gamma_N)$, $N \geq 2$, be a system of proper contractions on a complete metric space. Then there exists a unique self-similar non-empty compact subset $K$. We consider the union ${\mathcal G} = \cup_{i=1}^N…

We show that $B(H)$ for an infinite dimensional Hilbert space $H$ cannot be realized as the reduced twisted $C^*$-algebra of any locally compact Hausdorff \'etale groupoid. The proof is based on the canonical conditional expectation…

We present a general approach to a modular frame theory in C*-algebras and Hilbert C*-modules. The investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal Hilbert…

We find first structural background information about the reasons that for any C*-algebra $A$ and any two Hilbert $A$-modules $M \subseteq N$ with $M^\perp=\{0\}$, every bounded $A$-linear map $N \to A$ (or $N \to N)$ vanishing on $M$ might…

We construct operator systems $\mathfrak C_I$ that are universal in the sense that all operator systems can be realized as their quotients. They satisfy the operator system lifting property. Without relying on the theorem by Kirchberg, we…

We consider positive semidefinite kernels valued in the $*$-algebra of continuous and continuously adjointable operators on a VH-space (Vector Hilbert space in the sense of Loynes) and that are invariant under actions of $*$-semigroups. For…

We give an order-theoretic characterization of the essential image of the forgetful functor from the category of real/complex unital C*-algebras to the category of real/complex unital operator systems. It is based on the characterization of…