Related papers: A Note on Operator Biprojectivity of Compact Quant…

Let $\mathbb K$ be an algebraically closed field of characteristic zero. Let $V$ be a module over the polynomial ring $\mathbb K[x,y]$. The actions of $x$ and $y$ determine linear operators $P$ and $Q$ on $V$ as a vector space over $\mathbb…

Let $G$ be a locally compact, Hausdorff, second countable groupoid and $A$ be a separable, $C_0(G^{(0)})$-nuclear, $G$-$C^*$-algebra. We prove the existence of quasi-invariant, completely positive and contractive lifts for equivariant,…

Let $A$ be a $C^*$-algebra. We say that $A$ satisfies the SP if every bounded homomorphism $A\to B(K)$, with $K$ a Hilbert space, is similar to a $*$-homomorphism. We introduce three hypotheses that relate to extending hyperreflexive…

Given a separable unital C*algebra $C$, let $E_n$ denote the Hilbert module equal to the completion of the Schwartz space of rapidly decreasing smooth functions from $R^n$ to $C$ equipped with the $C$-valued inner product given by…

We introduce an appropriate notion of inner amenability for locally compact quantum groups, study its basic properties, related notions, and examples arising from the bicrossed product construction. We relate these notions to homological…

In this paper we construct and study the representation theory of a Hopf C^*-algebra with approximate unit, which constitutes quantum analogue of a compact group C^*-algebra. The construction is done by first introducing a…

We initiate a mathematically rigorous study of Klein-Gordon position operators in single-particle relativistic quantum mechanics. Although not self-adjoint, these operators have real spectrum and enjoy a limited form of spectral…

For a topological group $G$, amenability can be characterized by the amenability of the convolution Banach algebra $L^1(G)$. Here a Banach algebra $A$ is called amenable if every bounded derivation from $A$ into any dual--type…

Let $X$ be a locally compact Hausdorff space, let $A$ be a partially ordered algebra, and let $\pi\colon \mathrm{C}_{\mathrm c}(X)\to A$ be a positive algebra homomorphism. Under conditions on $A$ that are satisfied in a good number of…

Hilbert--Lie groups are Lie groups whose Lie algebra is a real Hilbert space whose scalar product is invariant under the adjoint action. These infinite-dimensional Lie groups are the closest relatives to compact Lie groups. Here we study…

We study contractive projections, isometries, and real positive maps on algebras of operators on a Hilbert space. For example we find generalizations and variants of certain classical results on contractive projections on C*-algebras and…

Let $A$ be a finite-dimensional $\mathbb{C}$-algebra of finite global dimension and $\mathcal{A}$ be the category of finitely generated right $A$-modules. By using of the category of two-periodic projective complexes…

It is shown that a trace invariant projection map, i.e. a positive unital idempotent map, of a finite dimensional C*-algebra into itself is non-decomposable if and only if it is atomic, or equivalently not the sum of a 2-positive and a…

Motivated by asymptotic symmetry groups in general relativity, we consider projective unitary representations $\overline{\rho}$ of the Lie group $\mathrm{Diff}_c(M)$ of compactly supported diffeomorphisms of a smooth manifold $M$ that…

Let $G$ be a finitely generated group with polynomial growth, and let $\om$ be a weight, i.e. a sub-multiplicative function on $G$ with positive values. We study when the weighted group algebra $\ell^1(G,\om)$ is isomorphic to an operator…

We introduce and study a number of invariants of locally compact quantum groups defined by their scaling and modular groups and the spectrum of their modular elements. Focusing mainly on compact quantum groups we consider the question…

If G is a Lie group, let D(G) be the space of compactly supported smooth functions on G. Consider the bilinear map B : D(G) x D(G) -> D(G), (f,g) |-> f*g which takes a pair of test functions to their convolution. We show that B is…

For a locally compact group $H$ with a left Haar measure, we study variable Lebesgue algebra $\mathcal{L}^{p(\cdot)}(H)$ with respect to a convolution. We show that if $\mathcal{L}^{p(\cdot)}(H)$ has bounded exponent, then it contains a…

We propose a general framework to contract unitary dual of Lie groups via holomorphic quantization of their co-adjoint orbits. The sufficient condition for the contractability of a representation is expressed via cocycles on coadjoint…

An algebra is said to be quasi-directly finite when any left-invertible element in its unitization is automatically right-invertible. It is an old observation of Kaplansky that the von Neumann algebra of a discrete group has this property;…