caa a22 4500 386382891 CHVBK 20180307112048.0 cr unu---uuuuu 161130s1989 xx s 000 0 eng 10.1017/S0308210500023921 doi S0308210500023921 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500023921 Almost-Lp-projections and Lp isomorphisms [Elektronische Daten] Lp -summands and Lp -projections in Banach spaces have been studied by E. Behrends, who showed that for a fixed value of p, l ≦ p ≦ ∞, p ≠ 2, any two Lp -projections on a given Banach space E commute. Here we introduce the notion of almost-Lp -projections, and we establish a result which generalises Behrends' theorem, while also simplifying its proof. Almost-Lp-projections are then applied to the study of small-bound isomorphisms of Bochner LP -spaces. It is shown that if the Banach space E satisfies a geometric condition which, in the finite-dimensional case, reduces to the absence of non-trivial Lp-summands, then for separable measure spaces, the existence of a small-bound isomorphism between Lp (λ1, E) and LP(λ2, E) implies that these Bochner spaces are, in fact, isometric. Copyright © Royal Society of Edinburgh 1989 Cambern Michael Department of Mathematics, University of California, Santa Barbara, CA 93106, U.S.A. Jarosz Krzysztof Department of Mathematics, Southern Illinois University at Edwardsville, Edwardsville, IL 62026, U.S.A. Wodinski Georg Institut für Mathematik I, Freie Universität Berlin, Arnimalle 3, D-1000 Berlin 33, Germany Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 113/1-2(1989), 13-25 0308-2105 113:1-2<13 1989 113 PRM https://doi.org/10.1017/S0308210500023921 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500023921 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cambern Michael Department of Mathematics, University of California, Santa Barbara, CA 93106, U.S.A NATIONALLICENCE 700 1- Jarosz Krzysztof Department of Mathematics, Southern Illinois University at Edwardsville, Edwardsville, IL 62026, U.S.A NATIONALLICENCE 700 1- Wodinski Georg Institut für Mathematik I, Freie Universität Berlin, Arnimalle 3, D-1000 Berlin 33, Germany NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 113/1-2(1989), 13-25 0308-2105 113:1-2<13 1989 113 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge