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Displaying 381 – 400 of 1407

Extreme cases of weak type interpolation.

Evgeniy Pustylnik (2005)

Revista Matemática Iberoamericana

We consider quasilinear operators T of joint weak type (a, b; p, q) (in the sense of [2]) and study their properties on spaces Lφ,E with the norm||φ(t) f*(t)||Ê, where Ê is arbitrary rearrangement-invariant space with respect to the measure dt/t. A space Lφ,E is said to be "close" to one of the endpoints of interpolation if the corresponding Boyd index of this space is equal to 1/a or to 1/p. For all possible kinds of such "closeness", we give sharp estimates for the function ψ(t) so as to obtain...

Extreme compact operators from Orlicz spaces to $C (Ω)$

Shutao Chen, Marek Wisła (1993)

Commentationes Mathematicae Universitatis Carolinae

Let $E^{ϕ} (μ)$ be the subspace of finite elements of an Orlicz space endowed with the Luxemburg norm. The main theorem says that a compact linear operator $T : E^{ϕ} (μ) \to C (Ω)$ is extreme if and only if $T^{*} ω \in Ext B ({(E^{ϕ} (μ))}^{*})$ on a dense subset of $Ω$ , where $Ω$ is a compact Hausdorff topological space and $〈 T^{*} ω, x 〉 = (T x) (ω)$ . This is done via the description of the extreme points of the space of continuous functions $C (Ω, L^{ϕ} (μ))$ , $L^{ϕ} (μ)$ being an Orlicz space equipped with the Orlicz norm (conjugate to the Luxemburg one). There is also given a theorem on closedness of the set of extreme...

Extreme contractions on certain function spaces

Anzelm Iwanik (1978)

Colloquium Mathematicum

Extreme points and rotundity of Orlicz-Sobolev spaces.

Chen, Shutao, Hu, Changying, Zhao, Charles Xuejin (2002)

International Journal of Mathematics and Mathematical Sciences

Extreme points of the Besicovitch--Orlicz space of almost periodic functions equipped with the Luxemburg norm

Slimane Hassaine, Fatiha Boulahia (2021)

Commentationes Mathematicae Universitatis Carolinae

We investigate which points in the unit sphere of the Besicovitch--Orlicz space of almost periodic functions, equipped with the Luxemburg norm, are extreme points. Sufficient conditions for the strict convexity of this space are also given.

Extreme points of the positive part of the unit ball and strictly monotone norm.

Ryszard Grzaslewicz, Helmut H. Schaefer (1991)

Mathematische Zeitschrift

Extreme points of the unit cell in Lebesgue-Bochner function spaces

Kondagunta Sundaresan (1970)

Colloquium Mathematicae

Extremely Non-Nice Operators into CK and Continuous Mappings into the Hilbert Cube.

S. Koppelberg, P. Greim (1984/1985)

Mathematische Zeitschrift

Factorisation des applications $Λ p$ -sommantes

P. Assouad (1973/1974)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

Factorisation des isomorphies d’ordre des espaces $L^{p}$

Marouan Ajlani (1969/1970)

Séminaire Choquet. Initiation à l'analyse

Factorization of vector measures and their integration operators

José Rodríguez (2016)

Colloquium Mathematicae

Let X be a Banach space and ν a countably additive X-valued measure defined on a σ-algebra. We discuss some generation properties of the Banach space L¹(ν) and its connection with uniform Eberlein compacta. In this way, we provide a new proof that L¹(ν) is weakly compactly generated and embeds isomorphically into a Hilbert generated Banach space. The Davis-Figiel-Johnson-Pełczyński factorization of the integration operator $I_{ν} : L ¹ (ν) \to X$ is also analyzed. As a result, we prove that if $I_{ν}$ is both completely continuous...

Factorization theorem for $1$ -summing operators

Irene Ferrando (2011)

Czechoslovak Mathematical Journal

We study some classes of summing operators between spaces of integrable functions with respect to a vector measure in order to prove a factorization theorem for $1$ -summing operators between Banach spaces.

Fenchel-Orlicz spaces [Book]

Barry Turett (1980)

Fine behavior of functions whose gradients are in an Orlicz space

Jan Malý, David Swanson, William P. Ziemer (2009)

Studia Mathematica

For functions whose derivatives belong to an Orlicz space, we develop their "fine" properties as a generalization of the treatment found in [MZ] for Sobolev functions. Of particular importance is Theorem 8.8, which is used in the development in [MSZ] of the coarea formula for such functions.

Finite dimensional subspaces of $L_{p}$

D. Lewis (1978)

Studia Mathematica

Fixed point theorems for generalized Lipschitzian semigroups in Banach spaces.

Thakur, Balwant Singh, Jung, Jong Soo (1999)

International Journal of Mathematics and Mathematical Sciences

Fixed point theorems for nonexpansive mappings in modular spaces

Poom Kumam (2004)

Archivum Mathematicum

In this paper, we extend several concepts from geometry of Banach spaces to modular spaces. With a careful generalization, we can cover all corresponding results in the former setting. Main result we prove says that if $ρ$ is a convex, $ρ$ -complete modular space satisfying the Fatou property and $ρ_{r}$ -uniformly convex for all $r > 0$ , C a convex, $ρ$ -closed, $ρ$ -bounded subset of $X_{ρ}$ , $T : C \to C$ a $ρ$ -nonexpansive mapping, then $T$ has a fixed point.

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