\(L_p [0,1] \setminus \underset {q>p} \bigcup L_q [0,1]\) is spaceable for every \(p > 0\)
From MaRDI portal
Publication:417411
DOI10.1016/j.laa.2011.12.028zbMath1246.46016OpenAlexW43223572MaRDI QIDQ417411
Juan B. Seoane-Sepúlveda, Daniel M. Pellegrino, Vinícius Vieira Fávaro, Geraldo Botelho
Publication date: 14 May 2012
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.laa.2011.12.028
Normed linear spaces and Banach spaces; Banach lattices (46B99) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30)
Related Items (20)
Lineability and spaceability: a new approach ⋮ Spaceability on some classes of Banach spaces ⋮ Large structures in certain subsets of Orlicz spaces ⋮ A note on latticeability and algebrability ⋮ Lineability and unbounded, continuous and integrable functions ⋮ A general lineability criterion for complements of vector spaces ⋮ Unnamed Item ⋮ Spaceablity in weak Morrey spaces ⋮ General criteria for a stronger notion of lineability ⋮ On the spaceability of the set of functions in the Lebesgue space \(L_p\) which are not in \(L_q\) ⋮ Non-Lipschitz functions with bounded gradient and related problems ⋮ Spaceability of strict order integrability ⋮ Lineability criteria, with applications ⋮ On sequences not enjoying Schur's property ⋮ A spaceability result in the context of hypergroups ⋮ Disjoint dynamics of weighted translations on solid spaces ⋮ Algebraic structure of continuous, unbounded and integrable functions ⋮ Nonlinear subsets of function spaces and spaceability ⋮ Algebrability, non-linear properties, and special functions ⋮ Linear subsets of nonlinear sets in topological vector spaces
Cites Work
This page was built for publication: \(L_p [0,1] \setminus \underset {q>p} \bigcup L_q [0,1]\) is spaceable for every \(p > 0\)
