Spaceability in Banach and quasi-Banach sequence spaces
By G. Botelho, D. Diniz, V. V. Fávaro, Daniel Pellegrino. 2010
49 citations recorded by the source corpus.
Abstract Let X be a Banach space. We prove that, for a large class of Banach or quasi-Banach spaces E of X -valued sequences, the sets E - ⋃ q ∈ Γ l q ( X ) , where Γ is any subset of ( 0 , ∞ ] , and E - c 0 ( X ) contain closed infinite-dimensional subspaces of E (if non-empty, of course). This result is applied in several particular cases and it is also shown that the same technique can be used to improve a result on the existence of spaces formed by norm-attaining linear operators.
Subfields: Geometry and Topology, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/8171ec7cc4600c3ff30596a5c3b68a2edc6db003
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Citations in the corpus
- Lineability criteria, with applications (2013, background): “not q-integrable for some p, q ∈ (0,+∞], see for instance [11], [30], [31], [39], [40], [41], [42], [54], [55], [57] and [58].”
- Linear subsets of nonlinear sets in topological vector spaces (2013, result): “More precisely, in [84] Bernal-González and Ordóñez-Cabrera provided a series of conditions on a measure space (Ω,Σ, μ) to ensure the spaceability of the sets Lp(Ω)\ ⋃ q∈[1,p) Lq(Ω), Lp(Ω)\ ⋃ q∈[p,∞) Lq(Ω), and Lp(Ω) \ ⋃ q∈[1,∞)\{p} Lq(μ,X) (for p ≥ 1); whereas in [111] Botelho, Fávaro, Pellegri”