Related papers: A footnote on Expanding maps
In this paper we begin the study of some important Banach spaces of slice hyperholomorphic functions, namely the Bloch, Besov and weighted Bergman spaces, and we also consider the Dirichlet space, which is a Hilbert space. The importance of…
The paper considers some concepts of trichotomy with different growth rates for evolution operators in Banach spaces. Connections between these concepts and characterizations in terms of Lyapunov- type norms are given.
We establish a spectral characterization theorem for the operators on complex Hilbert spaces of arbitrary dimensions that attain their norm on every closed subspace. The class of these operators is not closed under addition. Nevertheless,…
We describe the spaces $H^1(R)$ and BMO$(R)$ in terms of their closely related, simpler dyadic and two-sided counterparts. As a result of these characterizations we establish when a bounded linear operator defined on dyadic or two-sided…
We establish necessary and sufficient conditions for the boundedness and compactness of weighted composition operators acting on weighted Dirichlet spaces and determine the spectrum of a certain class of such operators. Our results extend…
This paper is a sequel to [6]. In that paper we transferred the discussions in [1] and [13] concerning almost invariant half-spaces for operators on complex Banach spaces to the context of operators on Hilbert space, and we gave easier…
In this paper we recontextualize the theory of matrix weights within the setting of Banach lattices. We define an intrinsic notion of directional Banach function spaces, generalizing matrix weighted Lebesgue spaces. Moreover, we prove an…
In this paper we give conditions under which sub differential limits can be better estimated.
We outline the scheme for quantization of classical Banach space results associated with some prototypes of dynamical maps and describe the quantization of correlations as well. A relation between these two areas is discussed.
(Revised version, January 2006. S. Gouezel pointed out that, when 1<r<2, the proof in the previous version was incomplete. In fixing this gap, we simplified the argument in Section 6. In addition, there is a new appendix, with an…
We establish complete characterizations of various notions of expansivity for weighted composition operators on a very general class of locally convex spaces of continuous functions. This class includes several classical classes of…
These notes are formal. Here, in this abstract, not in the note, we should say that all that is in the text was done, essentially, by Aleksander Pe{\l}czy\'nski. BUT: Anyhow, a new notion of an O-frame for an operator is introduced. For the…
In this note we study Banach spaces of traces of real polynomials on $\mathbb R^n$ to compact subsets equipped with supremum norms from the point of view of Geometric Functional Analysis.
In this survey, we consider Banach spaces of analytic functions in one and several complex variables for which: (i) polynomials are dense, (ii) point-evaluations on the domain are bounded linear functionals, and (iii) the shift operator…
We consider linear operators defined on a subspace of a complex Banach space into its topological antidual acting positively in a natural sense. The goal of this paper is to investigate of this kind of operators. The main theorem is a…
We study the statistical properties of piecewise expanding maps in the general setting of metric measure spaces. We provide sufficient conditions for exponential mixing of such systems with explicit estimates on the constants. We also…
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…
This paper investigates mapping spaces between enriched operads and relates these spaces to those between operadic bimodules via convenient fiber sequences. The main statements hold for simplicial operads, operads enriched in simplicial…
We show that a representation of a Banach algebra $A$ on a Banach space $X$ can be extended to a canonical representation of $A^{**}$ on $X$ if and only if certain orbit maps $A\to X$ are weakly compact. When this is the case, we show that…
The present note is a corrigendum to the paper "On Smooth extensions of vector-valued functions defined on closed subsets of Banach spaces" [Math. Ann. (2013) 355: 1201--1219].