Related papers: Hypercyclic differentiation operators

We study best approximations in Banach spaces via Birkhoff-James orthogonality of functionals. To exhibit the usefulness of Birkhoff-James orthogonality techniques in the study of best approximation problems, some algorithms and distance…

We build on the work by Davies, extending the Helffer-Sj\"ostrand Functional Calculus domain for semi-bounded operators on Banach spaces given a priori controlled growth of the resolvents. We employ Seeley's Extension Theorem to extend…

We establish a theory of NC functions on a class of von Neumann algebras with a particular direct sum property, e.g. $B(\mathcal{H})$. In contrast to the theory's origins, we do not rely on appealing to results from the matricial case. We…

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 give a simple proof of the Baillon-Haddad theorem for convex functions defined on open and convex subsets of Hilbert spaces. We also state some generalizations and limitations. In particular, we discuss equivalent characterizations of…

Generalizing classical results of the theory of absolutely summing operators, in this paper we characterize the duals of a quite large class of Banach operator ideals defined or characterized by the transformation of vector-valued…

Let T and C be two Hilbert space operators. We prove that if T is near, in a certain sense, to an operator completely polynomially dominated with a finite bound by C, then T is similar to an operator which is completely polynomially…

The purpose of this note is to show that, if $\mcB$ is a uniformly convex Banach, then the dual space $\mcB'$ has a "Hilbert space representation" (defined in the paper), that makes $\mcB$ much closer to a Hilbert space then previously…

According to Grivaux, the group $GL(X)$ of invertible linear operators on a separable infinite dimensional Banach space $X$ acts transitively on the set $\Sigma(X)$ of countable dense linearly independent subsets of $X$. As a consequence,…

A necessary and sufficient condition for an operator space to support a multiplication making it completely isometric and isomorphic to a unital operator algebra is proved. The condition involves only the holomorphic structure of the Banach…

We show that the existence of a strongly convex function with a Lipschitz derivative on a Banach space already implies that the space is isomorphic to a Hilbert space. Similarly, if both a function and its convex conjugate are $C^2$ then…

We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…

In this paper we generalize the classical theorems of Brown and Halmos about algebraic properties of Toeplitz operators to Bergman spaces over the unit ball in several complex variables. A key result, which is of independent interest, is…

Structural properties are given for $D(K)$, the Banach algebra of (complex) differences of bounded semi-continuous functons on a metric space $K$. For example, it is proved that if all finite derived sets of $K$ are non-empty, then a…

We develop a version of Herbrand's theorem for continuous logic and use it to prove that definable functions in infinite-dimensional Hilbert spaces are piecewise approximable by affine functions. We obtain similar results for definable…

Assume that $A$ is a closed linear operator defined on all of a Hilbert space $H$. Then $A$ is bounded. A new short proof of this classical theorem is given on the basis of the uniform boundedness principle. The proof can be easily extended…

We investigate operators between spaces of holomorphic functions in several complex variables. Let $G_1, G_2 \subset \mathbb{C}^n$ be cylindrical domains. We construct a canonical map from the space of bounded linear operators…

We give orthonormal characterizations of collectively compact (limited) sets of linear operators from a Hilbert space to a Banach space.

The classical Hahn-Banach theorem is based on a successive point-by-point procedure of extending bounded linear functionals. In the setting of a general metric domain, the conditions are less restrictive and the extension is only required…

In this paper, for a generalised shift operator introduced earlier, we prove theorem of coincidence of classes of functions defined by the order of best approximation by algebraical polynomials and the generalised Lipschitz classes defined…