Related papers: Operators on a non locally compact group algebra

Denote by $SL_3(\mathbb R)$ the special linear group of degree 3 over the real numbers, $A$ the subgroup consisting of the diagonal matrices with positive entries. In this paper, we study the algebraic and analytic properties of the…

In this paper we introduce a very general setting dealing with the superposition of operators of any positive order and provide a systematic study of them. We also provide examples and counterexamples, as well as characterizing properties…

In this paper we introduce and study some Hilbert-type operators acting from the function spaces into the sequence spaces. We give some sufficient and necessary conditions for the boundedness and compactness of these Hilbert-type operators.…

Let $\A$ and $\B$ be operator algebras with $c_0$-isomorphic diagonals and let $\K$ denote the compact operators. We show that if $\A\otimes\K$ and $\B\otimes\K$ are isometrically isomorphic, then $\A$ and $\B$ are isometrically isomorphic.…

The algebraic notion of a differential operator on a module over a commutative ring is not extended to a module over a noncommutative ring.

We define a class of spaces on which one may generalise the notion of compactness following motivating examples from higher-dimensional number theory. We establish analogues of several well-known topological results (such as Tychonoff's…

In this paper we initiate the study of composition operators on the noncommutative Hardy space $H^2_{\bf ball}$. Several classical results about composition operators (boundedness, norm estimates, spectral properties, compactness,…

Remarks are given to the structure of physical states in 2D gravity coupled to $C\leq 1$ matter. The operator algebra of the discrete state operators is calculated for the theory with non-vanishing cosmological constant.

We discuss and develop some connections between analysis on singular spaces and operator algebras, as presented in my sequence of four lectures at the conference "Noncommutative geometry and applications," Frascati, Italy, June 16-21, 2014.…

Let $G$ be the identity component of the isometry group for an arbitrary curved two-point homogeneous space $M$. We consider algebras of $G$-invariant differential operators on bundles of unit spheres over $M$. The generators of this…

In this paper, we study the structure of closed algebraic ideals in the algebra of operators acting on a Lorentz sequence space.

For a locally compact group $G$ we consider the algebra $CD(G)$ of convolution dominated operators on $L^{2}(G)$: An operator $A:L^2(G)\to L^2(G)$ is called convolution dominated if there exists $a\in L^1(G)$ such that for all $f \in…

Leibniz algebras are non-skewsymmetric analogue of Lie algebras. In this paper, we consider weighted relative Rota-Baxter operators on Leibniz algebras. We define cohomology of such operators and as an application, we study their…

The relations between $L^{\pm}$ operators and the generators in the quantum enveloping algebras are studied. The $L^{\pm}$ operators for $U_{q}A_{N}$ and $U_{q}G_{2}$ algebras are explicitly expressed by the generators as examples.

Unbounded composition operators in $L^2$-space over discrete measure spaces are investigated. Normal, formally normal and quasinormal composition operators acting in $L^2$-spaces of this kind are characterized.

Let $(X, T^{1,0}X)$ be a connected orientable compact CR manifold of dimension $2n+1$, $n \geq 1$ with non-degenerate Levi curvature. In this paper, we study the algebra of Toeplitz operators on $X$ and we establish star product for some…

We consider semigroups of continuous, surjective, locally injective maps of a compact metric space, and whether such semigroups admit a transfer operator.

We summarize and deepen recent results on systems of orthogonal pure states on operator algebras. Especially, we focus on noncommutative generalizations of some principles of topology of locally compact spaces such as exposining points by…

A p-local compact group is an algebraic object modelled on the p-local homotopy theory of classifying spaces of compact Lie groups and p-compact groups. In the study of these objects unstable Adams operations, are of fundamental importance.…

The nature of so-called differential-algebraic operators and their approximations is constitutive for the direct treatment of higher-index differential-algebraic equations. We treat first-order differential-algebraic operators in detail and…