Yevgen Ivakhno, “On sets with extremely big slices”, Zh. Mat. Fiz. Anal. Geom., 2006, Volume 2, Number 1,Pages <nobr>94

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On sets with extremely big slices

Yevgen Ivakhno

Department of Mechanics and Mathematics, V.N. Karazin Kharkov National University, 4 Svobody Sq., Kharkov, 61077, Ukraine

Abstract: A new characterization of the Radon-Nikodym property in terms of sizes of slices and equivalent norms is presented. A property opposite to the Radon–Nikodym property is studied in the context of 1-unconditional sums of Banach spaces.

Key words and phrases: Radon–Nikodym property, big slice property, 1-unconditional sums of Banach spaces.

MSC: 46B20, 46B22, 46G10, 46B03

Received: 29.03.2005

Language: English