Related papers: Spectral theorems for positive algebra homomorphis…
Let $A$ be a C*-algebra that is the norm closure $A = \overline{\sum_{\beta \in \alpha} I_\beta}$ of an arbitrary sum of C*-ideals $I_\beta \subseteq A$. We construct a homological spectral sequence that takes as input the K-theory of…
We study the question when for a given *-algebra $\mathcal{A}$ a sequence of cones $C_n\in M_n(\mathcal{A})$ can be realized as cones of positive operators in a faithful *-representation of $\mathcal{A}$ on a Hilbert space. A…
Continuous mappings between compact Hausdorff spaces can be studied using homomorphisms between algebraic structures (lattices, Boolean algebras) associated with the spaces. This gives us more tools with which to tackle problems about these…
We provide a partial classification of positive linear maps in matrix algebras which is based on a family of spectral conditions. This construction generalizes celebrated Choi example of a map which is positive but not completely positive.…
We prove the following statement: Let $X=\text{SL}_n(\mathbb{Z})\backslash \text{SL}_n(\mathbb{R})$, and consider the standard action of the diagonal group $A<\text{SL}_n(\mathbb{R})$ on it. Let $\mu$ be an $A$-invariant probability measure…
We show that unitary representations of simply connected, semisimple algebraic groups over local fields of characteristic zero obey a spectral gap absorption principle: that is, that spectral gap is preserved under tensor products. We do…
Let R be a von Neumann algebra acting on a Hilbert space H and let R_sa be the set of selfadjoint elements of R. It is well known that R_sa is a lattice with respect to the usual partial order ≤ if and only if R is abelian. We define…
Let $A^p_\omega$ denote the Bergman space in the unit disc induced by a radial weight~$\omega$ with the doubling property $\int_{r}^1\omega(s)\,ds\le C\int_{\frac{1+r}{2}}^1\omega(s)\,ds$. The positive Borel measures such that the…
Joint spectra of tuples of operators are subsets in complex projective space. The corresponding tuple of operators can be viewed as an infinite dimensional analog of a determinantal representation of the joint spectrum. We investigate the…
Given a compact metric space X and a unital C*-algebra A, we introduce a family of seminorms on the C*-algebra of continuous functions from X to A, denoted C(X, A), induced by classical Lipschitz seminorms that produce compact quantum…
It is shown that any finite-dimensional homomorphic image of an inverse limit of nilpotent not-necessarily-associative algebras over a field is nilpotent. More generally, this is true of algebras over a general commutative ring k, with…
The notion of a coalgebra measuring, introduced by Sweedler, is a kind of generalized ring map between algebras. We begin by studying maps on Hochschild homology induced by coalgebra measurings. We then introduce a notion of coalgebra…
This is an introduction to the algebras $A\subset B(H)$ that the linear operators $T:H\to H$ can form, once a complex Hilbert space $H$ is given. Motivated by quantum mechanics, we are mainly interested in the von Neumann algebras, which…
To each regular affine building there is naturally associated a commutative algebra A spanned by vertex set averaging operators. In this paper we study the algebra homomorphisms from A into the complex numbers. In particular, we provide two…
The essence of the potential algebra concept [3] is that quantum mechanical free motions of scalar particles on curved surfaces of given isometry algebras can be mapped on 1D Schroedinger equations with particular potentials. As long as the…
This work will be centered in commutative Banach subalgebras of the algebra of bounded linear operators defined on a Free Banach spaces of countable type. The main goal of this work wil be to formulate a representation theorem for these…
Given a subspace $U\subset\mathbb{C}[x_1,\dots,x_n]_d$ we consider the closure of the image of the rational map $\mathbb{P}^{n-1}\dashrightarrow\mathbb{P}^{\dim U-1}$ given by $U$. Its coordinate ring is isomorphic to $\bigoplus_{i\ge 0}…
We establish a spectral characterization theorem for the operators on complex Hilbert spaces of arbitrary dimensions that attain their norm on every closed subspace. The class of these operators is not closed under addition. Nevertheless,…
Let $A$ be a $C^*$-algebra and $E\colon A \to A$ a conditional expectation. The Kadison-Schwarz inequality for completely positive maps, $$E(x)^*E(x) \leq E(x^* x),$$ implies that $$ \|E(x)\|^2 \leq \|E(x^* x)\|.$$ In this note we show that…
Given a finitely-generated group $\pi$ and a linear algebraic group $G$, the representation variety Hom$(\pi,G)$ has a natural filtration by the characteristic varieties associated to a rational representation of $G$. Its algebraic…