Generalized perfect spaces

Calabuig, J. M.; Delgado, O.; Pérez, Enrique Alfonso Sánchez

doi:10.1016/s0019-3577(09)00008-1

Cited by 27 publications

(54 citation statements)

References 9 publications

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“…In this case, by (iv), for all 0 < δ < 1, there exist Ψ ∈ Y (2) and Ψ 2 ∈ Y (2) such that Ψ(δu) ≤ Φ(u) ≤ Ψ(u), Ψ 2 (δu) ≤ Φ 2 (u) ≤ Ψ 2 (u) for all u.…”

Section: Lemma 3 If φ ∈ Y (1) ∪ Ymentioning

confidence: 99%

“…We will prove a similar result for simple functions; it is important to note that we don't assume explicitly the Δ 2 -condition. (2) and x = 0 is a simple function, then I Φ (x/ x Φ ) = 1.…”

Section: If φ ∈ Y (1) ∪ Y (2) Then φ Is Continuous Strictly Increamentioning

confidence: 99%

“…To prove the theorem we collect some properties of Φ and its inverse: (3) and 0 < δ < 1, then there exists a Young function Ψ ∈ Y (2) such that b(Φ) = b(Ψ) and…”

Section: Lemma 3 If φ ∈ Y (1) ∪ Ymentioning

confidence: 99%

“…on Ω (in particular, X = {0}). Several properties and some calculated concrete examples we can find in the paper by Maligranda and Persson [6] (see also Nakai [7] and Calabuig, Delgado, and Sánchez Pérez [2] …”

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confidence: 99%

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Pointwise multipliers of Orlicz spaces

Maligrańda

Nakai

2010

Arch. Math.

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Abstract. We show that the result on multipliers of Orlicz spaces holds in general. Namely, under the assumption that three Young functions Φ1, Φ2 and Φ, generating corresponding Orlicz spaces, satisfy the esti-The result with some restrictions either on Young functions or on the measure μ was proved by Maligranda and Persson (Indag. Math. 51 (1989), 323-338). Our result holds for any collection of three Young functions satisfying the above estimate and for an arbitrary complete σ-finite measure μ. Mathematics Subject Classification (2000). 46E30, 46B42.

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“…In this case, by (iv), for all 0 < δ < 1, there exist Ψ ∈ Y (2) and Ψ 2 ∈ Y (2) such that Ψ(δu) ≤ Φ(u) ≤ Ψ(u), Ψ 2 (δu) ≤ Φ 2 (u) ≤ Ψ 2 (u) for all u.…”

Section: Lemma 3 If φ ∈ Y (1) ∪ Ymentioning

confidence: 99%

Section: If φ ∈ Y (1) ∪ Y (2) Then φ Is Continuous Strictly Increamentioning

confidence: 99%

“…To prove the theorem we collect some properties of Φ and its inverse: (3) and 0 < δ < 1, then there exists a Young function Ψ ∈ Y (2) such that b(Φ) = b(Ψ) and…”

Section: Lemma 3 If φ ∈ Y (1) ∪ Ymentioning

confidence: 99%

mentioning

confidence: 99%

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Pointwise multipliers of Orlicz spaces

Maligrańda

Nakai

2010

Arch. Math.

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“…The main differences are that we change tensor products of Banach spaces by products of function spaces, and the usual Banach space duality by the generalized duality for Banach function spaces (see [4,17,24]). Recently, a new effort has been made in order to develop the theory of products of Banach function spaces and general multiplication operators, that are a particular -but central-case of the general factorization norms and spaces that we develop here.…”

Section: Introductionmentioning

confidence: 99%

Factorization Theorems for Multiplication Operators on Banach Function Spaces

Pérez

2014

Integr. Equ. Oper. Theory

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Abstract. Let X Y and Z be Banach function spaces over a measure space (Ω, Σ, µ). Consider the spaces of multiplication operators X Y from X into the Köthe dual Y of Y , and the spaces X Z and Z Y defined in the same way. In this paper we introduce the notion of factorization norm as a norm on the product space X Z · Z Y ⊆ X Y that is defined from some particular factorization scheme related to Z. In this framework, a strong factorization theorem for multiplication operators is an equality between product spaces with different factorization norms. Lozanovskii, Reisner and Maurey-Rosenthal theorems are considered in our arguments to provide examples and tools for assuring some requirements. We analyze the class d * p,Z of factorization norms, proving some factorization theorems for them when p-convexity/p-concavity type properties of the spaces involved are assumed. Some applications in the setting of the product spaces are given.Mathematics Subject Classification (2010). Primary 46E30; Secondary 47B38, 46B42, 46B28.

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The weak topology on q‐convex Banach function spaces

Albesa

Calabuig

Pérez

2011

Mathematische Nachrichten

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Let X(μ) be a Banach function space. In this paper we introduce two new geometric notions, q‐convexity and weak q‐convexity associated to a subset S of the unit ball of the dual of X(μ), 1 ≤ q < ∞. We prove that in the general case both notions are not equivalent and we study the relation between them, showing that they can be used for describing the weak topology in these spaces. We define the canonical q‐concave weak topology τq on X(μ)—a topology generated by q‐concave seminorms—for obtaining our main result: A σ‐order continuous Banach function space X(μ) is q‐convex if and only if the following topological inclusions τw⊆τq⊆τ‖ · ‖ hold. As an application, in the last section we prove a suitable Maurey‐Rosenthal type factorization theorem for operators from a Banach function space X(μ) into a Banach space that holds under weaker assumptions on the q‐convexity requirements for X(μ).

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Generalized perfect spaces

Cited by 27 publications

References 9 publications

Pointwise multipliers of Orlicz spaces

Pointwise multipliers of Orlicz spaces

Factorization Theorems for Multiplication Operators on Banach Function Spaces

The weak topology on q‐convex Banach function spaces

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