Ultrafilters over \(N\) and operators on \(L^ 1\)

DOI10.1216/RMJM/1181072080zbMath0869.46007OpenAlexW1981313605MaRDI QIDQ1815511

Minos A. Petrakis

Publication date: 12 November 1996

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/rmj/Vol26-2/CONT26-2/CONT26-2.html

zbMATH Keywords

CCPfinite-dimensional decompositionDunford-PettisRademacher tree

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Linear operators defined by compactness properties (47B07) Linear operators on function spaces (general) (47B38) Radon-Nikodým, Kre?n-Milman and related properties (46B22)

Cites Work

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• Dentability, trees, and Dunford-Pettis operators on \(L_ 1\)
• Dunford-Pettis operators on \(L^ 1\) and the Radon-Nikodym property
• A characterization of non-Dunford-Pettis operators on \(L^ 1\).
• Representations of convex non-dentable sets
• Discrepancy norms on the space \(M[0,1\) of Radon measures]
• Martingales, \(G_{delta}\)-embeddings and quotients of \(L_1\).
• Slices, RNP, strong regularity, and martingales
• Dentability and finite-dimensional decompositions
• Ultraproducts in Banach space theory.

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