Related papers: Dilations and constrained algebras

Infinite-dimensional Galilean conformal algebras can be constructed by contracting pairs of symmetry algebras in conformal field theory, such as $W$-algebras. Known examples include contractions of pairs of the Virasoro algebra, its $N=1$…

We call an operator algebra A {\em reversible} if A with reversed multiplication is also an abstract operator algebra (in the modern operator space sense). This class of operator algebras is intimately related to the {\em symmetric operator…

For any Inonu-Wigner contraction of a three dimensional Lie algebra we construct the corresponding contractions of representations. Our method is quite canonical in the sense that in all cases we deal with realizations of the…

Let $\phi$ be an isometric automorphism of the non-commutative disc algebra $\fA_n$ for $n \geq 2$. We show that every contractive covariant representation of $(\fA_n, \phi)$ dilates to a unitary covariant representation of $(\O_n, \phi)$.…

An algebra $A$ is said to be directly finite if each left invertible element in the (conditional) unitization of $A$ is right invertible. We show that the reduced group ${\rm C}^\ast$-algebra of a unimodular group is directly finite,…

Suppose that f is a projective birational morphism with at most one-dimensional fibres between d-dimensional varieties X and Y, satisfying ${\bf R}f_* \mathcal{O}_X = \mathcal{O}_Y$. Consider the locus L in Y over which f is not an…

We determine the derived representation types of algebras with radical square zero and give a description of the indecomposable objects in their bounded derived categories.

Let p be a polynomial in one variable. It is shown that the universal C*-algebra of the relation p(x)=0, \|x\| \le C is semiprojective, residually finite-dimensional and has trivial extension group.

We extend Agler's notion of a function algebra defined in terms of test functions to include products, in analogy with the practice in real algebraic geometry, and hence the term preordering in the title. This is done over abstract sets and…

Under very general conditions it is shown that if $A$ is a uniform algebra generated by real-analytic functions, then either $A$ consists of all continuous functions or else there exists a disc on which every function in $A$ is holomorphic.…

We consider the structure of algebra of operators, acting in $n-$fold tensor product space, which are partially transposed on the last term. Using purely algebraical methods we show that this algebra is semi-simple and then, considering its…

The weak operator topology closed operator algebra on $L^2(R)$ generated by the one-parameter semigroups for translation, dilation and multiplication by $exp(i\lambda x), \lambda \geq 0$, is shown to be a reflexive operator algebra, in the…

We investigate the representation and complete representation classes for algebras of partial functions with the signature of relative complement and domain restriction. We provide and prove the correctness of a finite equational…

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…

We consider contractions of Lie and Poisson algebras and the behaviour of their centres under contractions. A polynomial Poisson algebra A=K[W] is said to be of Kostant type, if its centre Z(A) is freely generated by homogeneous polynomials…

We exhibit a singly generated, semisimple commutative operator algebra with a contractive approximate identity, such that the spectrum of the generator is a null sequence and zero, but the algebra is not the closed linear span of the…

We develop contractive finite dimensional realizations for rational matrix functions of one variable on domains that are not simply connected, such as the annulus. The proof uses multivariable contractive realization results as well as…

Let $f: B^n \rightarrow {\mathbb R}$ be a $d+1$ times continuously differentiable function on the unit ball $B^n$, with $\max_{z\in B^n} \| f(z) \|=1$. A well-known fact is that if $f$ vanishes on a set $Z\subset B^n$ with a non-empty…

For an analytic function $f(z)$ on the unit disk $|z|<1$ with $f(0)=f'(0)-1=0$ and $f(z)\ne0, 0<|z|<1,$ we consider the power deformation $f_c(z)=z(f(z)/z)^c$ for a complex number $c.$ We determine those values $c$ for which the operator…

(1) Let $A$ be an operator on a space ${\cal H}$ of even finite dimension. Then for some decomposition ${\cal H}={\cal F}\oplus{\cal F}^{\perp}$, the compressions of $A$ onto ${\cal F}$ and ${\cal F}^{\perp}$ are unitarily equivalent. (2)…