On isometric domains of positive operators on -spaces
Ryszard Grząślewicz (1987)
Colloquium Mathematicae
Similarity:
Ryszard Grząślewicz (1987)
Colloquium Mathematicae
Similarity:
Changsun Choi, Anna Kamińska, Han Ju Lee (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
Similarity:
We give sufficient and necessary conditions for complex extreme points of the unit ball of Orlicz-Lorentz spaces, as well as we find criteria for the complex rotundity and uniform complex rotundity of these spaces. As an application we show that the set of norm-attaining operators is dense in the space of bounded linear operators from into d(w,1), where is a predual of a complex Lorentz sequence space d(w,1), if and only if wi ∈ c₀∖ℓ₂.
Marian Nowak (2011)
Banach Center Publications
Similarity:
Let (Ω,Σ,μ) be a finite measure space and let X be a real Banach space. Let be the Orlicz-Bochner space defined by a Young function Φ. We study the relationships between Dunford-Pettis operators T from L¹(X) to a Banach space Y and the compactness properties of the operators T restricted to . In particular, it is shown that if X is a reflexive Banach space, then a bounded linear operator T:L¹(X) → Y is Dunford-Pettis if and only if T restricted to is -compact.
Bojan Magajna (1993)
Studia Mathematica
Similarity:
Given two n-tuples and of bounded linear operators on a Hilbert space the question of when there exists an elementary operator E such that for all j =1,...,n, is studied. The analogous question for left multiplications (instead of elementary operators) is answered in any C*-algebra A, as a consequence of the characterization of closed left A-submodules in .
Marian Nowak, Agnieszka Oelke (2008)
Banach Center Publications
Similarity:
We study linear operators from a non-locally convex Orlicz space to a Banach space . Recall that a linear operator is said to be σ-smooth whenever in implies . It is shown that every σ-smooth operator factors through the inclusion map , where Φ̅ denotes the convex minorant of Φ. We obtain the Bochner integral representation of σ-smooth operators . This extends some earlier results of J. J. Uhl concerning the Bochner integral representation of linear operators defined on...
L. Aharouch, E. Azroul, M. Rhoudaf (2006)
Applicationes Mathematicae
Similarity:
We prove the existence of solutions of the unilateral problem for equations of the type Au - divϕ(u) = μ in Orlicz spaces, where A is a Leray-Lions operator defined on , and .
Jin Cai Wang (2003)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
We use Simonenko quantitative indices of an -function to estimate two parameters and in Orlicz function spaces with Orlicz norm, and get the following inequality: , where and are Simonenko indices. A similar inequality is obtained in with Orlicz norm.
Jan A. Rempała (1990)
Annales Polonici Mathematici
Similarity:
Pei-Kee Lin, Huiying Sun (1997)
Annales Polonici Mathematici
Similarity:
Let ϕ: ℝ → ℝ₊ ∪ 0 be an even convex continuous function with ϕ(0) = 0 and ϕ(u) > 0 for all u > 0 and let w be a weight function. u₀ and v₀ are defined by u₀ = supu: ϕ is linear on (0,u), v₀=supv: w is constant on (0,v) (where sup∅ = 0). We prove the following theorem. Theorem. Suppose that (respectively, ) is an order continuous Lorentz-Orlicz space. (1) has normal structure if and only if u₀ = 0 (respectively, (2) has weakly normal structure if and only if .
Andrzej Kasperski (2005)
Banach Center Publications
Similarity:
We introduce the Musielak-Orlicz space of multifunctions and the set of φ-integrable selections of F. We show that some decomposable sets in Musielak-Orlicz space belong to . We generalize Theorem 3.1 from [6]. Also, we get some theorems on the space and the set .
Dumitru Popa (2014)
Studia Mathematica
Similarity:
We use the Maurey-Rosenthal factorization theorem to obtain a new characterization of multiple 2-summing operators on a product of spaces. This characterization is used to show that multiple s-summing operators on a product of spaces with values in a Hilbert space are characterized by the boundedness of a natural multilinear functional (1 ≤ s ≤ 2). We use these results to show that there exist many natural multiple s-summing operators such that none of the associated linear operators...
(2011)
Banach Center Publications
Similarity:
Let E be a Banach function space over a finite and atomless measure space (Ω,Σ,μ) and let and be real Banach spaces. A linear operator T acting from the Köthe-Bochner space E(X) to Y is said to be absolutely continuous if whenever μ(Aₙ) → 0, (Aₙ) ⊂ Σ. In this paper we examine absolutely continuous operators from E(X) to Y. Moreover, we establish relationships between different classes of linear operators from E(X) to Y.
Anna Kamińska, Karol Leśnik, Yves Raynaud (2014)
Studia Mathematica
Similarity:
For an Orlicz function φ and a decreasing weight w, two intrinsic exact descriptions are presented for the norm in the Köthe dual of the Orlicz-Lorentz function space or the sequence space , equipped with either the Luxemburg or Amemiya norms. The first description is via the modular , where f* is the decreasing rearrangement of f, ≺ denotes submajorization, and φ⁎ is the complementary function to φ. The second description is in terms of the modular ,where (f*)⁰ is Halperin’s level...
Z. D. Ren (2010)
Annales Polonici Mathematici
Similarity:
A new lower bound for the Jung constant of the Orlicz sequence space defined by an N-function Φ is found. It is proved that if is reflexive and the function tΦ’(t)/Φ(t) is increasing on , then . Examples in Section 3 show that the above estimate is better than in Zhang’s paper (2003) in some cases and that the results given in Yan’s paper (2004) are not accurate.
Ibrahim Akbarbaglu, Saeid Maghsoudi (2012)
Colloquium Mathematicae
Similarity:
Let G be a locally compact group with a fixed left Haar measure. Given Young functions φ and ψ, we consider the Orlicz spaces and on a non-unimodular group G, and, among other things, we prove that under mild conditions on φ and ψ, the set is well defined on G is σ-c-lower porous in . This answers a question raised by Głąb and Strobin in 2010 in a more general setting of Orlicz spaces. We also prove a similar result for non-compact locally compact groups.
Ioana Ghenciu, Paul Lewis (2008)
Bulletin of the Polish Academy of Sciences. Mathematics
Similarity:
Results of Emmanuele and Drewnowski are used to study the containment of c₀ in the space , as well as the complementation of the space of w*-w compact operators in the space of w*-w operators from X* to Y.
Agnieszka Kałamajska, Katarzyna Pietruska-Pałuba (2006)
Colloquium Mathematicae
Similarity:
We obtain interpolation inequalities for derivatives: , and their counterparts expressed in Orlicz norms: ||∇f||²(q,α) ≤ C||Φ₁(x,|f|,|∇(2)f|)||(p,β) ||Φ₂(x,|f|,|∇(2)f|)||(r,γ)where is the Orlicz norm relative to the function . The parameters p,q,r,α,β,γ and the Carathéodory functions Φ₁,Φ₂ are supposed to satisfy certain consistency conditions. Some of the classical Gagliardo-Nirenberg inequalities follow as a special case. Gagliardo-Nirenberg inequalities in logarithmic spaces...
Ron Kerman, Luboš Pick (2011)
Studia Mathematica
Similarity:
We study imbeddings of the Sobolev space : = u: Ω → ℝ with < ∞ when |α| ≤ m, in which Ω is a bounded Lipschitz domain in ℝⁿ, ϱ is a rearrangement-invariant (r.i.) norm and 1 ≤ m ≤ n - 1. For such a space we have shown there exist r.i. norms, and , that are optimal with respect to the inclusions . General formulas for and are obtained using the -method of interpolation. These lead to explicit expressions when ϱ is a Lorentz Gamma norm or an Orlicz norm.
Barry Turett
Similarity:
CONTENTSIntroduction............................................................................... 51. Definitions and preliminary results......................................... 72. Completeness of .............................. 93. Linear functionals on ....................... 264. Geometry of Fenchel-Orlicz spaces........................................ 41References....................................................................................... 54
E. Harboure, O. Salinas, B. Viviani (2002)
Colloquium Mathematicae
Similarity:
Let ϕ and ψ be functions defined on [0,∞) taking the value zero at zero and with non-negative continuous derivative. Under very mild extra assumptions we find necessary and sufficient conditions for the fractional maximal operator , associated to an open bounded set Ω, to be bounded from the Orlicz space into , 0 ≤ α < n. For functions ϕ of finite upper type these results can be extended to the Hilbert transform f̃ on the one-dimensional torus and to the fractional integral operator...
N. Kalton (1993)
Studia Mathematica
Similarity:
We examine conditions under which a pair of rearrangement invariant function spaces on [0,1] or [0,∞) form a Calderón couple. A very general criterion is developed to determine whether such a pair is a Calderón couple, with numerous applications. We give, for example, a complete classification of those spaces X which form a Calderón couple with We specialize our results to Orlicz spaces and are able to give necessary and sufficient conditions on an Orlicz function F so that the pair...
Ron Kerman, Luboš Pick (2008)
Studia Mathematica
Similarity:
We find necessary and sufficient conditions on a pair of rearrangement-invariant norms, ϱ and σ, in order that the Sobolev space be compactly imbedded into the rearrangement-invariant space , where Ω is a bounded domain in ℝⁿ with Lipschitz boundary and 1 ≤ m ≤ n-1. In particular, we establish the equivalence of the compactness of the Sobolev imbedding with the compactness of a certain Hardy operator from into . The results are illustrated with examples in which ϱ and σ are both...
Nguyen Thanh Chung (2015)
Annales Polonici Mathematici
Similarity:
We consider Kirchhoff type problems of the form ⎧ -M(ρ(u))(div(a(|∇u|)∇u) - a(|u|)u) = K(x)f(u) in Ω ⎨ ⎩ ∂u/∂ν = 0 on ∂Ω where , N ≥ 3, is a smooth bounded domain, ν is the outward unit normal to ∂Ω, , M: [0,∞) → ℝ is a continuous function, , and f: ℝ → ℝ is a continuous function not satisfying the Ambrosetti-Rabinowitz type condition. Using variational methods, we obtain some existence and multiplicity results.
Maciej Burnecki (2008)
Banach Center Publications
Similarity:
We consider an embedding of the group of invertible transformations of [0,1] into the algebra of bounded linear operators on an Orlicz space. We show that if this embedding preserves the group action then the Orlicz space is an -space for some 1 ≤ p < ∞.
Joan Cerdà, Joaquim Martín, Pilar Silvestre (2011)
Banach Center Publications
Similarity:
If C is a capacity on a measurable space, we prove that the restriction of the K-functional to quasicontinuous functions f ∈ QC is equivalent to . We apply this result to identify the interpolation space .
Teresa Winiarska, Tadeusz Winiarski (2003)
Annales Polonici Mathematici
Similarity:
The purpose of this paper is to provide a method of reduction of some problems concerning families of linear operators with domains to a problem in which all the operators have the same domain . To do it we propose to construct a family of automorphisms of a given Banach space X having two properties: (i) the mapping is sufficiently regular and (ii) for t ∈ . Three effective constructions are presented: for elliptic operators of second order with the Robin boundary condition...
Pascal Lefèvre, Daniel Li, Hervé Queffélec, Luis Rodríguez-Piazza (2011)
Studia Mathematica
Similarity:
We study the canonical injection from the Hardy-Orlicz space into the Bergman-Orlicz space .