Search results for "vector"
showing 10 items of 2660 documents
Description of the limit set of Henstock–Kurzweil integral sums of vector-valued functions
2015
Abstract Let f be a function defined on [ 0 , 1 ] and taking values in a Banach space X . We show that the limit set I HK ( f ) of Henstock–Kurzweil integral sums is non-empty and convex when the function f has an integrable majorant and X is separable. In the same setting we give a complete description of the limit set.
VECTOR-VALUED FUNCTIONS INTEGRABLE WITH RESPECT TO BILINEAR MAPS
2008
Let $(\Omega, \Sigma, \mu)$ be a $\sigma-$finite measure space, $1\le p \lt \infty$, $X$ be a Banach space $X$ and ${\cal B} :X\times Y \to Z$ be a bounded bilinear map. We say that an $X$-valued function $f$ is $p-$integrable with respect to ${\cal B}$ whenever $\sup\{\int_\Omega\|{\cal B}(f(w),y)\|^pd\mu: \|y\|=1\}$ is finite. We identify the spaces of functions integrable with respect to the bilinear maps arising from H\"older's and Young's inequalities. We apply the theory to give conditions on $X$-valued kernels for the boundedness of integral operators $T_{{\cal B}}(f) (w)=\int_{\Omega'}{{\cal B}}(k(w,w'),$ $f(w'))d\mu'(w')$ from ${\mathrm L}^p(Y)$ into ${\mathrm L}^p(Z)$, extending t…
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.
Tangency conditions for multivalued mappings
1996
We prove that interiority conditions imply tangency conditions for two multivalued mappings from a topological space into a normed vector space. As a consequence, we obtain the lower semicontinuity of the intersection of two multivalued mappings. An application to the epi-upper semicontinuity of the sum of convex vector-valued mappings is given.
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.
On the structure of the ultradistributions of Beurling type
2008
Let O be a nonempty open set of the k-dimensional euclidean space Rk. In this paper, we give a structure theorem on the ultradistributions of Beurling type in O. Also, other structure results on certain ultradistributions are obtained, in terms of complex Borel measures in O.
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.
Closedness and lower semicontinuity of positive sesquilinear forms
2009
The relationship between the notion of closedness, lower semicontinuity and completeness (of a quotient) of the domain of a positive sesquilinear form defined on a subspace of a topological vector space is investigated and sufficient conditions for their equivalence are given.