Search results for "COMPOSITION"

Norm, essential norm and weak compactness of weighted composition operators between dual Banach spaces of analytic functions

2017

Abstract In this paper we estimate the norm and the essential norm of weighted composition operators from a large class of – non-necessarily reflexive – Banach spaces of analytic functions on the open unit disk into weighted type Banach spaces of analytic functions and Bloch type spaces. We also show the equivalence of compactness and weak compactness of weighted composition operators from these weighted type spaces into a class of Banach spaces of analytic functions, that includes a large family of conformally invariant spaces like BMOA and analytic Besov spaces.

Shrinking and boundedly complete Schauder frames in Fréchet spaces

2014

We study Schauder frames in Fréchet spaces and their duals, as well as perturbation results. We define shrinking and boundedly complete Schauder frames on a locally convex space, study the duality of these two concepts and their relation with the reflexivity of the space. We characterize when an unconditional Schauder frame is shrinking or boundedly complete in terms of properties of the space. Several examples of concrete Schauder frames in function spaces are also presented.

Fredholm composition operators on algebras of analytic functions on Banach spaces

2010

AbstractWe prove that Fredholm composition operators acting on the uniform algebra H∞(BE) of bounded analytic functions on the open unit ball of a complex Banach space E with the approximation property are invertible and arise from analytic automorphisms of the ball.

The surjective hull of a polynomial ideal

2016

The aim of this paper is the study of surjective ideals of homogeneous polynomials between Banach spaces. To do so we define the surjective hull of a polynomial ideal and prove the main properties of this hull procedure. For a more comprehensive theory, new lifting properties of homogeneous polynomials are proved and applied to the description of the surjective hulls of the ideals of I-bounded polynomials and of composition polynomials ideals. Several applications are provided.

Composition operators on uniform algebras, essential norms, and hyperbolically bounded sets

2006

Let A be a uniform algebra, and let o be a self-map of the spectrum M A of A that induces a composition operator C o on A. The object of this paper is to relate the notion of "hyperbolic boundedness" introduced by the authors in 2004 to the essential spectrum of C o . It is shown that the essential spectral radius of C o , is strictly less than 1 if and only if the image of M A under some iterate o n of o is hyperbolically bounded. The set of composition operators is partitioned into "hyperbolic vicinities" that are clopen with respect to the essential operator norm. This partition is related to the analogous partition with respect to the uniform operator norm.

An algebraic loop theorem and the decomposition of PD 3 -pairs

2006

A Decomposition Theorem for the Fuzzy Henstock Integral

2012

We study the fuzzy Henstock and the fuzzy McShane integrals for fuzzy-number valued functions. The main purpose of this paper is to establish the following decomposition theorem: a fuzzy-number valued function is fuzzy Henstock integrable if and only if it can be represented as a sum of a fuzzy McShane integrable fuzzy-number valued function and of a fuzzy Henstock integrable fuzzy number valued function generated by a Henstock integrable function.

A Decomposition of Henstock-Kurzweil-Pettis Integrable Multifunctions

2009

We proved in our earlier paper [9] that in case of separable Banach space-valued multifunctions each Henstock-Kurzweil-Pettis integrable multifunction can be represented as a sum of one of its Henstock-Kurzweil-Pettis integrable selectors and a Pettis integrable multifunction. Now, we prove that the same result can be achieved in case of an arbitrary Banach space. Applying the representation theorem we describe the multipliers of the Henstock-Kurzweil-Pettis integrable multifunctions. Then we use this description to obtain a characterization of the Henstock-Kurzweil-Pettis integrability in terms of subadditive operators.

Varieties of almost polynomial growth: classifying their subvarieties

2007

Let G be the infinite dimensional Grassmann algebra over a field F of characteristic zero and UT2 the algebra of 2 x 2 upper triangular matrices over F. The relevance of these algebras in PI-theory relies on the fact that they generate the only two varieties of almost polynomial growth, i.e., they grow exponentially but any proper subvariety grows polynomially. In this paper we completely classify, up to PI-equivalence, the associative algebras A such that A is an element of Var(G) or A is an element of Var(UT2).

A characterization of the Schur property through the disk algebra

2017

[EN] In this paper we give a new characterization of when a Banach space E has the Schur property in terms of the disk algebra. We prove that E has the Schur property if and only if A(D, E) = A(D,E-w). (C) 2016 Elsevier Inc. All rights reserved.