Subspaces of \(L_ p\), \(p > 2\), with unconditional bases have equivalent partition and weight norms

DOI10.1007/S00013-005-1457-0zbMATH Open1097.46003arXivmath/0310343OpenAlexW2019425011MaRDI QIDQ818727

Simei Tong, Dale Alspach

Publication date: 21 March 2006

Published in: Archiv der Mathematik (Search for Journal in Brave)

Abstract: In this note we give a simple proof that every subspace of L_p, 2<p<infinity, with an unconditional basis has an equivalent norm determined by partitions and weights. Consequently L_p has a norm determined by partitions and weights.

Full work available at URL: https://arxiv.org/abs/math/0310343

zbMATH Keywords

unconditional basisnorm determined by partitions and weights

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) Isomorphic theory (including renorming) of Banach spaces (46B03)

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Subspaces of L_p, p>2, determined by partitions and weights

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