Search results for "Finite-rank operator"
showing 10 items of 32 documents
Two-dimensional Banach spaces with polynomial numerical index zero
2009
We study two-dimensional Banach spaces with polynomial numerical indices equal to zero.
Dynamics of differentiation and integration operators on weighted spaces of entire functions
2014
On ergodic operator means in Banach spaces
2016
We consider a large class of operator means and prove that a number of ergodic theorems, as well as growth estimates known for particular cases, continue to hold in the general context under fairly mild regularity conditions. The methods developed in the paper not only yield a new approach based on a general point of view, but also lead to results that are new, even in the context of the classical Cesaro means.
Weakly compact composition operators between algebras of bounded analytic functions
1999
Domains of accretive operators in Banach spaces
2016
LetD(A)be the domain of anm-accretive operatorAon a Banach spaceE. We provide sufficient conditions for the closure ofD(A)to be convex and forD(A)to coincide withEitself. Several related results and pertinent examples are also included.
A note on the Banach space of preregular maps
2011
The aim of this paper is to give simple proofs for Jeurnink's characterizations of preregular maps in terms of Θ-maps acting between Banach lattices. For Banach lattices E and F, we achieve our goal by considering the space Lβ(E, F) of all those linear maps T: E → F for which there exists a constant K such that {double pipe}Vn i=1 {pipe}Txi{pipe} ≤ K {double pipe}Vn i=1{pipe}xi for all finite sequences x1, ..., xn e{open}E. We show that, if Lβ(E; F), and the spaces L Θ (E; F) of Θ -map and Lpr(E; F) of preregular maps are respectively endowed with their canonical norms, then they are identical Banach spaces
On the operators which are invertible modulo an operator ideal
2001
Atkinson [3] studied the operators which are left invertible $i(X, Y) or right invertible $T{X, Y) modulo /C, with K. the compact operators. He proved that an operator T € C(X, Y) belongs to <£/ or $ r if and only if the kernel and the range of T are complemented and additionally, the kernel is finite dimensional or the range is finite codimensional, respectively. Yood [19] obtained some perturbation results for these classes and Lebow and Schechter [12] proved that the inessential operators form the perturbation class for $,(A") and $r{X). Yang [18] extended some results of ^3, 19] to operators invertible modulo W, with W the weakly compact operators. His aim was to study a generalised Fre…
Restricted Uniform Boundedness in Banach Spaces
2009
Precise conditions for a subset A of a Banach space X are known in order that pointwise bounded on A sequences of bounded linear functionals on X are uniformly bounded. In this paper, we study such conditions under the extra assumption that the functionals belong to a given linear subspace Γ of X *. When Γ = X *, these conditions are known to be the same ones assuring a bounded linear operator into X , having A in its image, to be onto. We prove that, for A , deciding uniform boundedness of sequences in Γ is the same property as deciding surjectivity for certain classes of operators. Keywords: Uniform boundedness; thick set; boundedness deciding set Quaestiones Mathematicae 32(2…
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.
The Bishop–Phelps–Bollobás property for operators from c0 into some Banach spaces
2017
Abstract We exhibit a new class of Banach spaces Y such that the pair ( c 0 , Y ) has the Bishop–Phelps–Bollobas property for operators. This class contains uniformly convex Banach spaces and spaces with the property β of Lindenstrauss. We also provide new examples of spaces in this class.