Related papers: Compact $AC(\sigma)$ operators

We prove the existence of algebras of hypercyclic vectors in three cases: convolution operators, composition operators, and backward shift operators.

An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.

We study the $H$-convergence of nonlocal linear operators in fractional divergence form, where the oscillations of the matrices are prescribed outside the reference domain. Our compactness argument bypasses the failure of the classical…

We give a short proof of the fact that each homogeneous linear differential operator $A$ of constant rank admits a homogeneous potential operator $B$, meaning that $\ker A(x)=\mathrm{im\,}B(x)$ for $x\neq 0$. We make some refinements of the…

This note characterizes both boundedness and compactness of a composition operator between any two analytic Campanato spaces on the unit complex disk.

Let G be a connected, compact, semisimple Lie group. It is known that for a compact closed orientable surface $\Sigma$ of genus $l >1$, the order of the group $H^2(\Sigma,\pi_1(G))$ is equal to the number of connected components of the…

In this paper we introduce a new decomposition of power-bounded operators, analogous to the Jacobs-deLeeuw-Glicksberg decomposition. This is done using so-called K\"ohler semigroups and the general theory of right topological compact…

We present several characterizations of $\sigma$-compact Hattori spaces, and reject some possible characterization candidates of the spaces.

This paper characterises the boundedness and compactness of Agler--McCarthy monomial operators by reducing them to weighted composition operators and deriving explicit Carleson measure criteria on the half-plane. The results are illustrated…

The commutators of bilinear Calder\'on-Zygmund operators and point-wise multiplication with a symbol in $cmo$ are bilinear compact operators on product of Lebesgue spaces. This work shows that, for certain non-degenerate Calder\'on-Zygmund…

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…

We characterize the compactness of commutators in the Bloom setting. Namely, for a suitably non-degenerate Calder\'on--Zygmund operator $T$, and a pair of weights $ \sigma , \omega \in A_p$, the commutator $ [T, b]$ is compact from $ L ^{p}…

The tractability of certain CSPs for dense or sparse instances is known from the 90s. Recently, the densification and the sparsification of CSPs were formulated as computational tasks and the systematical study of their computational…

In this short note, we present certain generalized versions of the commutator formulas of some natural operators on manifolds, and give some applications.

In this note we obtain commutativity criteria for normal compact operators using the projective spectrum. We thus improve a corresponding result obtained by Chagouel, Stessin and Zhu[Trans AMS,2016].

In this paper, we obtain a complete characterization for the compact difference of two composition operators acting on Bergman spaces with weight $\omega=e^{-\eta}$, $\Delta\eta>0$ in terms of the $\eta$-derived pseudodistance of two…

We consider commuting squares of finite dimensional von Neumann algebras having the algebra of complex numbers in the lower left corner. Examples include the vertex models, the spin models (in the sense of subfactor theory) and the…

We study the existence of a common hypercyclic vector for different families of composition operators.

Deformation spaces Hom($\pi$,G)/G of representations of the fundamental group $\pi$ of a surface $\Sigma$ in a Lie group $G$ admit natural actions of the mapping class group $Mod_\Sigma$, preserving a Poisson structure. When $G$ is compact,…

We study a version of the functional Hodrick-Prescott filter where the associated operator is not necessarily compact, but merely closed and densely defined with closed range. We show that the associated optimal smoothing operator preserves…