Related papers: On conjugate systems with respect to completely po…
We study the algebra of invariant differential operators on a certain homogeneous vector bundle over a Riemannian symmetric space of type $A_2$. We computed radial parts of its generators explicitly to obtain matrix-valued commuting…
In the current paper, we generalize the "compact operator" part of the Voiculescu's non-commutative Weyl-von Neumann theorem on approximate equivalence of unital $*$-homomorphisms of an commutative C$^*$ algebra $\mathcal{A}$ into a…
In this short note, we construct an exotic example of a locally compact group $G$ with a Borel $2$-cocycle $\omega$ such that the non-twisted group von Neumann algebra $L(G)$ is a factor, while the twisted group von Neumann algebra…
We consider a net of *-algebras, locally around any point of observation, equipped with a natural partial order related to the isotony property. Assuming the underlying manifold of the net to be a differentiable, this net shall be…
We show that a partition of the unity (or POVM) on a Hilbert space that is almost orthogonal is close to an orthogonal POVM in the same von Neumann algebra. This generalizes to infinite dimension previous results in matrix algebras by…
Given commuting families of Hermitian matrices {A1, ..., Ak} and {B1, ...., Bk}, conditions for the existence of a completely positive map L, such that L(Aj) = Bj for j = 1, ...,k, are studied. Additional properties such as unital or / and…
Motivated by existence problems for dissipative systems arising naturally in lattice models from quantum statistical mechanics, we consider the following $C^{\ast}$-algebraic setting: A given hermitian dissipative mapping $\delta$ is…
The centralizer algebra of a matrix consists of those matrices that commute with it. We investigate the basic representation-theoretic invariants of centralizer algebras, namely their radicals, projective indecomposable modules, injective…
It is shown that each linear operator on a separable Hilbert space which generates a finite type I von Neumann algebra has, up to unitary equivalence, a unique representation as a direct integral of inflations of mutually unitary…
Let g be a complex semisimple Lie algebra and let G' be the Langlands dual group. We give a description of the cohomology algebra of an arbitrary spherical Schubert variety in the loop Grassmannian for G' as a quotient of the form…
The Wigner-von Neumann method, which was previously used for perturbing continuous Schr\"{o}dinger operators, is here applied to their discrete counterparts. In particular, we consider perturbations of arbitrary $T$-periodic Jacobi…
We characterize covariant positive decomposable maps between unital C*-algebras in terms of a dilation theorem, which generalizes a seminal result by H. Scutaru from Rep. Math. Phys. 16 (1):79-87, 1979. As a case study, we provide a certain…
We show that if (A,a) and (B,b) are automorphic multivariable C*-dynamical systems with isometrically isomorphic tensor algebras (or semi crossed products), then the systems are piecewise conjugate over their Jacobson spectrum. This answers…
The covariance between real finite variance random variables can be expressed as the commutator of taking expectations and multiplying, both viewed as operators extended to act jointly on pairs of functions. The efficient influence curve of…
In this paper, we consider representations induced by general positive and completely positive sesquilinear maps with values in ordered Banach bimodules, such as the space of trace-class operators and the spaces of bounded linear operators…
Commuting maps on a class of algebras called inflated algebras are investigated. In particular, we can prove that every commuting map $\theta$ on such an algebra is of the form $\theta(x)=c x+\mu(x)$, where $c$ belongs to the base field $K$…
We study the general properties of commutative differential graded algebras in the category of representations over a reductive algebraic group with an injective central cocharacter. Besides describing the derived category of differential…
Let $B$ be a finitely generated algebra over a field $k$. Then $B$ is called a Jacobson algebra if every semiprime ideal of $B$ is semiprimitive. We will discuss several conditions, all involving the commutant of simple $B$-modules, which…
In commutative algebra, a Weitzenb\"ock derivation is a nonzero triangular linear derivation of the polynomial algebra $K[x_1,...,x_m]$ in several variables over a field $K$ of characteristic 0. The classical theorem of Weitzenb\"ock states…
By using a coherent state quantization of paragrassmann variables, operators are constructed in finite Hilbert spaces. We thus obtain in a straightforward way a matrix representation of the paragrassmann algebra. This algebra of finite…