Weak precompactness, strong boundedness, and weak complete continuity

DOI10.1017/S030500410006919XzbMath0737.46008OpenAlexW2077046933MaRDI QIDQ4712215

Paul W. Lewis, Elizabeth M. Bator, Catherine A. Abbott, Russell G. Bilyeu

Publication date: 25 June 1992

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s030500410006919x

zbMATH Keywords

uniform integrabilitystrongly bounded operatorsspace of Bochner integrable functionsuniform countable additivityweakly completely continuous operatorsabstract continuous function spacesoperators having weakly precompact adjointsweak precompactness in spaces of vector measures

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Spaces of vector- and operator-valued functions (46E40) Linear operators defined by compactness properties (47B07) Spaces of measures (46E27) Compactness in topological linear spaces; angelic spaces, etc. (46A50)

Related Items (10)

Extension of continuous linear operators on C_b(X, E) ⋮ Strongly bounded operators on \(C_{rc}(X,E)\) with the strict topology \(\beta_\sigma\) ⋮ A Riesz representation theory for completely regular Hausdorff spaces and its applications ⋮ Ideal exhaustiveness, weak convergence and weak compactness in Banach spaces ⋮ Completely continuous operators and the strict topology ⋮ Operators Having Weakly Precompact Adjoints ⋮ Conditional weak compactness in vector-valued function spaces ⋮ Operators on the space of bounded strongly measurable functions ⋮ Some classes of continuous operators on spaces of bounded vector-valued continuous functions with the strict topology ⋮ STRONGLY BOUNDED REPRESENTING MEASURES AND CONVERGENCE THEOREMS

Cites Work

• Unnamed Item
• Separable conjugate spaces
• An averaging result for \(l^ 1-\)sequences and applications to weakly conditionally compact sets in \(L^ 1\).
• Weak compactness in spaces of Bochner integrable functions and the Radon- Nikodym property
• Operators on continuous function spaces and convergence in the spaces of operators
• Weak Cauchy Sequences in L 1 (E)
• A Characterization of Banach Spaces Containing l ¹
• Linear Operators and Vector Measures
• Sur Les Applications Lineaires Faiblement Compactes D'Espaces Du Type C(K)

This page was built for publication: Weak precompactness, strong boundedness, and weak complete continuity