Search results for "BANACH SPACE"
showing 10 items of 281 documents
A property of connected Baire spaces
1997
Abstract We give a topological version of a classical result of F. Sunyer Balaguer's on a local characterization of real polynomials. This is done by studying a certain property on a class of connected Baire spaces, thus allowing us to obtain a local characterization of repeated integrals of analytic maps on Banach spaces.
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…
On some parameters related to weak noncompactness in L1(μ,E)
2009
Abstract A weak measure of noncompactness γU is defined in a Banach space in terms of convex compactness. We obtain relationships between the measure γU (A) of a bounded set A in the Bochner space L1 (μ,E) and two parameters Π(A) and Δ1(A). Then the criterion for relative weak compactness due to Ulger [19] and Diestel-Ruess-Schachermayer [11] is recovered.
Homomorphisms and composition operators on algebras of analytic functions of bounded type
2005
Abstract Let U and V be convex and balanced open subsets of the Banach spaces X and Y, respectively. In this paper we study the following question: given two Frechet algebras of holomorphic functions of bounded type on U and V, respectively, that are algebra isomorphic, can we deduce that X and Y (or X * and Y * ) are isomorphic? We prove that if X * or Y * has the approximation property and H wu ( U ) and H wu ( V ) are topologically algebra isomorphic, then X * and Y * are isomorphic (the converse being true when U and V are the whole space). We get analogous results for H b ( U ) and H b ( V ) , giving conditions under which an algebra isomorphism between H b ( X ) and H b ( Y ) is equiv…
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.
The Fixed Point Property in Banach Spaces with the NUS-Property
1997
Abstract In this paper, we show that the weak nearly uniform smooth Banach spaces have the fixed point property for nonexpansive mappings.
A unified Pietsch domination theorem
2008
In this paper we prove an abstract version of Pietsch's domination theorem which unify a number of known Pietsch-type domination theorems for classes of mappings that generalize the ideal of absolutely p-summing linear operators. A final result shows that Pietsch-type dominations are totally free from algebraic conditions, such as linearity, multilinearity, etc.
On generalized a-Browder's theorem
2007
We characterize the bounded linear operators T satisfying generalized a-Browder's theorem, or generalized a-Weyl's theorem, by means of localized SVEP, as well as by means of the quasi-nilpotent part H0(�I T) asbelongs to certain sets of C. In the last part we give a general framework in which generalized a-Weyl's theorem follows for several classes of operators. 1. Preliminaries. Let L(X) denote the space of bounded linear oper- ators on an infinite-dimensional complex Banach space X. For T ∈ L(X), denote by α(T) the dimension of the kernel ker T, and by β(T) the codi- mension of the range T(X). The operator T ∈ L(X) is called upper semi- Fredholm if α(T) < ∞ and T(X) is closed, and lower …
A Mönch type fixed point theorem under the interior condition
2009
Abstract In this paper we show that the well-known Monch fixed point theorem for non-self mappings remains valid if we replace the Leray–Schauder boundary condition by the interior condition. As a consequence, we obtain a partial generalization of Petryshyn's result for nonexpansive mappings.
Strict u-ideals in Banach spaces
2009
We study strict u-ideals in Banach spaces. A Banach space X is a strict u-ideal in its bidual when the canonical decomposition X = X X ? is unconditional. We characterize Banach spaces which are strict u-ideals in their bidual and show that if X is a strict u-ideal in a Banach space Y then X contains c0. We also show that '1 is not a u-ideal.