An ordinal \(L^p\)-index for Banach spaces, with application to complemented subspaces of \(L^p\)

DOI10.2307/1971293zbMath0496.46010OpenAlexW2002203388MaRDI QIDQ1170467

Jean Bourgain, Haskell P. Rosenthal, Gideon Schechtman

Publication date: 1981

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/1971293

zbMATH Keywords

martingalesordinal indexscript Lp spaceconstruct uncountably many mutually non-isomorphic complemented subspaces of Lplocal Lp-index

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20)

Related Items (18)

\({\mathcal COL}_p\) spaces -- the local structure of non-commutative \(L_p\) spaces ⋮ Non-isomorphic complemented subspaces of the reflexive Orlicz function spaces $L^{\Phi }[0,1$] ⋮ Some geometric aspects of operators acting from \(L_{1}\) ⋮ Ordinal indices of small subspaces of \(L_p\) ⋮ On the span of some three valued martingale difference sequences in \(L^ p\) \((1<p<\infty)\) and \(H^ 1\) ⋮ A history of solving some famous problems in mathematical analysis ⋮ The number of closed ideals in the algebra of bounded operators on Lebesgue spaces ⋮ Small subspaces of \(L_p\) ⋮ A new class of \(L^ 1-\)spaces ⋮ Subspaces and quotients of \(l_ p\) + \(l_ 2\) and \(X_ p\) ⋮ On the complemented subspaces of \(X_p\) ⋮ Independent sums of \(H_n^1(\mathbb{T})\) and \(H_n^1(\delta)\) ⋮ \({\mathcal{L}_1}\)-spaces with the Radon-Nikodým property containing reflexive subspaces ⋮ Ideals in \(L(L_1)\) ⋮ On the structure of Rosenthal's space \(X_\varphi\) in Orlicz function spaces ⋮ Unnamed Item ⋮ The SHAI property for the operators on \(L^p\) ⋮ Banach spaces for which the space of operators has 2^𝔠closed ideals

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