Search results for "BANACH SPACE"
showing 10 items of 281 documents
Single-valued extension property at the points of the approximate point spectrum
2003
Abstract A localized version of the single-valued extension property is studied at the points which are not limit points of the approximate point spectrum, as well as of the surjectivity spectrum. In particular, we shall characterize the single-valued extension property at a point λ o ∈ C in the case that λoI−T is of Kato type. From this characterizations we shall deduce several results on cluster points of some distinguished parts of the spectrum.
Operators Which Do Not Have the Single Valued Extension Property
2000
Abstract In this paper we shall consider the relationships between a local version of the single valued extension property of a bounded operator T ∈ L ( X ) on a Banach space X and some quantities associated with T which play an important role in Fredholm theory. In particular, we shall consider some conditions for which T does not have the single valued extension property at a point λ o ∈ C .
On set-valued cone absolutely summing maps
2009
Spaces of cone absolutely summing maps are generalizations of Bochner spaces Lp(μ, Y), where (Ω, Σ, μ) is some measure space, 1 ≤ p ≤ ∞ and Y is a Banach space. The Hiai-Umegaki space \( \mathcal{L}^1 \left[ {\sum ,cbf(X)} \right] \) of integrably bounded functions F: Ω → cbf(X), where the latter denotes the set of all convex bounded closed subsets of a separable Banach space X, is a set-valued analogue of L1(μ, X). The aim of this work is to introduce set-valued cone absolutely summing maps as a generalization of \( \mathcal{L}^1 \left[ {\sum ,cbf(X)} \right] \) , and to derive necessary and sufficient conditions for a set-valued map to be such a set-valued cone absolutely summing map. We …
AbsolutelyLexpq - Summing Norms of Diagonal Operators inlr and Limit Orders ofLexp - Summing Operators
2001
We compute the absolutely L – summing norms of the diagonal operators acting on lr (1 ≤ q, r < ∞) and determine the limit orders of the absolutely Lexp – summing operators.
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…
Existence of fixed points for the sum of two operators
2010
The purpose of this paper is to study the existence of fixed points for the sum of two nonlinear operators in the framework of real Banach spaces. Later on, we give some examples of applications of this type of results (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
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…
A decomposition theorem for compact-valued Henstock integral
2006
We prove that if X is a separable Banach space, then a measurable multifunction Γ : [0, 1] → ck(X) is Henstock integrable if and only if Γ can be represented as Γ = G + f, where G : [0, 1] → ck(X) is McShane integrable and f is a Henstock integrable selection of Γ.