Intersection of Lebesgue Spaces L 1 and L 2

DOI10.2307/2047108zbMath0661.46015OpenAlexW2000889646MaRDI QIDQ3810336

Stephen Dilworth

Publication date: 1988

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2047108

zbMATH Keywords

Schauder basiscomplementedcomplemented subspace isomorphic to \(\ell ^ 1\)isomorphic to Hilbert spacetranslated Haar system

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) Geometry and structure of normed linear spaces (46B20) Classical Banach spaces in the general theory (46B25) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15)

Related Items (3)

\(L_p + L_q\) and \(L_p \cap L_q\) are not isomorphic for all \(1 \leq p\), \(q\leq \infty\), \(p\neq q\) ⋮ 𝐿_{𝑝}+𝐿_{∞} and 𝐿_{𝑝}∩𝐿_{∞} are not isomorphic for all 1≤𝑝<∞, 𝑝≠2 ⋮ On various modes of scalar convergence in \(L_0({\mathfrak X})\)

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