Search results for "interpolation."
showing 10 items of 253 documents
On the construction of Ljusternik-Schnirelmann critical values in banach spaces
1991
w h e r e f a n d g are functionals on a Banach space X, are considered in many papers. The existence theorems are based on the existence of a critical vector with respect to the manifold M,={xEX: f(x)=r}. Morse theory can often be used to obtain precise information about the behaviour of the functional close to the critical level. However, this would limit the study to Hilbert spaces and functions with nondegenerate critical points. These assumptions are not always satisfied in applications and are not rleeded when applying the Ljusternik--Schnirelmann theory. Therefore, Ljusternik--Schnirelmann theory has been widely used to study various nonlinear eigenvalue problems. Very general result…
Vector-valued analytic functions of bounded mean oscillation and geometry of Banach spaces
1997
When dealing with vector-valued functions, sometimes is rather difficult to give non trivial examples, meaning examples which do not come from tensoring scalar-valued functions and vectors in the Banach space, belonging to certain classes. This is the situation for vector valued BMO. One of the objectives of this paper is to look for methods to produce such examples. Our main tool will be the vector-valued extension of the following result on multipliers, proved in [MP], which says that the space of multipliers between H and BMOA can be identified with the space of Bloch functions B, i.e. (H, BMOA) = B (see Section 3 for notation), which, in particular gives that g ∗ f ∈ BMOA whenever f ∈ H…
Sobolev classes of Banach space-valued functions and quasiconformal mappings
2001
We give a definition for the class of Sobolev functions from a metric measure space into a Banach space. We give various characterizations of Sobolev classes and study the absolute continuity in measure of Sobolev mappings in the “borderline case”. We show under rather weak assumptions on the source space that quasisymmetric homeomorphisms belong to a Sobolev space of borderline degree; in particular, they are absolutely continuous. This leads to an analytic characterization of quasiconformal mappings between Ahlfors regular Loewner spaces akin to the classical Euclidean situation. As a consequence, we deduce that quasisymmetric maps respect the Cheeger differentials of Lipschitz functions …
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.
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.
Injective spaces of real-valued functions with the baire property
1995
Generalizing the technique used by S.A. Argyros in [3], we give a lemma from which certain Banach spaces are shown to be non-injective. This is applied mainly to study the injectivity of spaces of real-valued Borel functions and functions with the Baire property on a topological space. The results obtained in this way do not follow from previous works about this matter.
Boundaries for algebras of analytic functions on function module Banach spaces
2013
We consider the uniform algebra of continuous and bounded functions that are analytic on the interior of the closed unit ball of a complex Banach function module X. We focus on norming subsets of , i.e., boundaries, for such algebra. In particular, if X is a dual complex Banach space whose centralizer is infinite-dimensional, then the intersection of all closed boundaries is empty. This also holds in case that X is an -sum of infinitely many Banach spaces and further, the torus is a boundary.
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.
Property (M) and the weak fixed point property
1997
It is shown that in Banach spaces with the property (M) of Kalton, nonexpansive self mappings of nonempty weakly compact convex sets necessarily have fixed points. The stability of this conclusion under renormings is examined and conditions for such spaces to have weak normal structure are considered.