Related papers: Cowen-Douglas operators and analytic continuation
We prove that every lattice homomorphism acting on a Banach space $\mathcal{X}$ with the lattice structure given by an unconditional basis has a non-trivial closed invariant subspace. In fact, it has a non-trivial closed invariant ideal,…
This paper is devoted to the study of two classes of operators related to disjointly weakly compact sets, which we call $DW$-DP operators and $DW$-limited operators, respectively. They carry disjointly weakly compact subsets of a Banach…
Let $\Gamma$ be an oriented Jordan smooth curve and $\alpha$ be a diffeomorphism of $\Gamma$ onto itself which has an arbitrary nonempty set of periodic points. We prove criteria for one-sided invertiblity of the binomial functional…
In this paper, we study a class of convolution operators on the space of distributions that enlarge the well-studied class of passive operators. In this larger class, we are able to associate, to each operator, a holomorphic function in the…
This paper considers the inversion of ill-posed linear operators. To regularise the problem the solution is enforced to lie in a non-convex subset. Theoretical properties for the stable inversion are derived and an iterative algorithm akin…
We identify concrete examples of hypercyclic generalised derivations acting on separable ideals of operators and establish some necessary conditions for their hypercyclicity. We also consider the dynamics of elementary operators acting on…
Starting from the study of pseudodifferential operators with completely periodic symbols, we obtain results of continuity and invertibility of a class of Gabor operators on time-frequency invariant Banach spaces. As an applications we find…
We study superdifferential operators of order $2n+1$ which are covariant with respect to superconformal changes of coordinates on a compact super Riemann surface. We show that all such operators arise from super M\"obius covariant ones. A…
We study the compactness of composition operators on the Bergman spaces of certain bounded convex domains in $\mathbb{C}^n$ with non-trivial analytic discs contained in the boundary. As a consequence we characterize that compactness of the…
We construct a stable right inverse for the divergence operator in non-cylindrical domains in space-time. The domains are assumed to be H\"older regular in space and evolve continuously in time. The inverse operator is of Bogovskij type,…
The question is addressed of when a Sobolev type space, built upon a general rearrangement-invariant norm, on an $n$-dimensional domain, is a Banach algebra under pointwise multiplication of functions. A sharp balance condition among the…
The object of this paper is to prove a version of the Beurling-Helson-Lowdenslager invariant subspace theorem for operators on certain Banach spaces of functions on a multiply connected domain in the complex plane. The norms for these…
In this work, we define a new class of fractional analytic functions containing functional parameters in the open unit disk. By employing this class, we introduce two types of fractional operators, differential and integral. The fractional…
We study linear operators on a finite-dimensional space whose Kippenhahn curves consist of concentric circles centered at the origin. We say that such operators have Circularity property. One class of examples is rotationally invariant…
Left-Alia algebras are a class of algebras with symmetric Jacobi identities. They contain several typical types of algebras as subclasses, and are closely related to the invariant theory. In this paper, we study the construction theory of…
We study the Ornstein-Uhlenbeck operator and the Ornstein-Uhlenbeck semigroup in an open convex subset of an infinite dimensional separable Banach space $X$. This is done by finite dimensional approximation. In particular we prove…
We analyze a definition of product of Banach spaces that is naturally associated by duality with an abstract notion of space of multiplication operators. This dual relation allows to understand several constructions coming from different…
In this paper we investigate the spectra and the ergodic properties of the multiplication operators and the convolution operators acting on the Schwartz space $\mathcal{S}(\mathbb{R})$ of rapidly decreasing functions, i.e., operators of the…
The duality of uniform approximation property for Banach spaces is well known. In this note, we establish, under the assumption of local reflexivity, the duality of uniform approximation property in the category of operator spaces.
This article consists of two connected parts. In the first part, we study the shift invariant subspaces in certain $\mathcal{P}^2(\mu)$-spaces, which are the closures of analytic polynomials in the Lebesgue spaces $\mathcal{L}^2(\mu)$…