Search results for "Infinite-dimensional vector function"
showing 10 items of 21 documents
Connected components in the space of composition operators onH∞ functions of many variables
2003
LetE be a complex Banach space with open unit ballBe. The structure of the space of composition operators on the Banach algebra H∞, of bounded analytic functions onBe with the uniform topology, is studied. We prove that the composition operators arising from mappings whose range lies strictly insideBe form a path connected component. WhenE is a Hilbert space or aCo(X)- space, the path connected components are shown to be the open balls of radius 2.
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
An integral for a banach valued function
2009
Abstract Using partitions of the unity ((PU)-partition), a new definition of an integral is given for a function f : [a, b] → X, where X is a Banach space, and it is proved that this integral is equivalent to the Bochner integral.
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…
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.
A note on banach partial *-algebras
2006
A Banach partial *-algebra is a locally convex partial *-algebra whose total space is a Banach space. A Banach partial *-algebra is said to be of type (B) if it possesses a generating family of multiplier spaces that are also Banach spaces. We describe the basic properties of such objects and display a number of examples, namely LP-like function spaces and spaces of operators on Hilbert scales.
A Riemann manifold structure of the spectra of weighted algebras of holomorphic functions
2009
[EN] In this paper we give general conditions on a countable family V of weights on an unbounded open set U in a complex Banach space X such that the weighted space HV (U) of holomorphic functions on U has a Frechet algebra structure. For such weights it is shown that the spectrum of HV(U) has a natural analytic manifold structure when X is a symmetrically regular Banach space, and in particular when X = C-n. (C) 2009 Elsevier Ltd. All rights reserved.
A space of projections on the Bergman space
2010
We define a set of projections on the Bergman space A 2 , which is parameterized by an ane subset of a Banach space of holomorphic functions in the disk and which includes the classical Forelli-Rudin projections.