On set-valued cone absolutely summing maps

• Autorzy: Coenraad Labuschagne , Valeria Marraffa
• Języki publikacji: EN

Abstrakty

EN

Spaces of cone absolutely summing maps are generalizations of Bochner spaces L p(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 L 1(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 also describe these set-valued cone absolutely summing maps as those that map order-Pettis integrable functions to integrably bounded set-valued functions.

Słowa kluczowe

EN

Banach lattice; Bochner space; Cone absolutely summing operator; Integrably bounded set-valued function; Set-valued operator

Kategorie tematyczne

• 47H04: Set-valued operators
• 28B15: Set functions, measures and integrals with values in ordered spaces
• 28B20: Set-valued set functions and measures; integration of set-valued functions; measurable selections
• 46B42: Banach lattices

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 1
• Strony: 148-157

Daty

wydano

2010-02-01

online

2010-02-02

Twórcy

autor

Coenraad Labuschagne

• University of the Witwatersrand

autor

Valeria Marraffa

• Università Degli Studi Di Palermo

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-009-0059-7