Uniqueness of the unconditional basis of \(\ell_{1}(\ell_p)\) and \(\ell_p(\ell_1)\), \(0

DOI10.1007/S11117-003-8542-ZzbMath1084.46002OpenAlexW2030018146MaRDI QIDQ1780509

Nigel J. Kalton, Fernando Albiac, Camino Leránoz

Publication date: 13 June 2005

Published in: Positivity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11117-003-8542-z

zbMATH Keywords

uniquenessquasi-Banach spaceunconditional basis

Mathematics Subject Classification ID

Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) (46A16) Banach lattices (46B42) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Banach sequence spaces (46B45)

Related Items (16)

Isomorphic classification of mixed sequence spaces and of Besov spaces over [0, 1^d] ⋮ Uniqueness of unconditional basis of infinite direct sums of quasi-Banach spaces ⋮ Uniqueness of unconditional basis of \(H_p(\mathbb{T}) \oplus \ell_2\) and \(H_p(\mathbb{T}) \oplus \mathcal{T}^{(2)}\) for \(0 < p < 1\) ⋮ Obituary: Nigel John Kalton, 1946-2010 ⋮ An alternative approach to the uniqueness of unconditional basis of \(\ell _p(c_{0})\) for \(0<p<1\) ⋮ Uniqueness of unconditional bases in nonlocally convex \(\ell _{1}\)-products ⋮ Projections and unconditional bases in direct sums of ℓp spaces, 0<p≤∞ ⋮ Uniqueness of unconditional basis in quasi-Banach spaces which are not sufficiently Euclidean ⋮ Uniqueness of symmetric basis in quasi-Banach spaces ⋮ The Tsirelson space \(\mathcal T(p)\) has a unique unconditional basis up to permutation for \(0<p<1\) ⋮ Uniqueness of unconditional bases in nonlocally convex \(c_0\)-products ⋮ On the mutually non isomorphic ℓp(ℓq) spaces, II ⋮ Uniqueness of unconditional basis in Lorentz sequence spaces ⋮ Greedy approximation for biorthogonal systems in quasi-Banach spaces ⋮ Addendum to: ``Uniqueness of unconditional basis of infinite direct sums of quasi-Banach spaces ⋮ On the permutative equivalence of squares of unconditional bases

Cites Work

• Uniqueness of unconditional bases in quasi-Banach spaces with applications to Hardy spaces
• Uniqueness of unconditional bases in Banach spaces
• Uniqueness of unconditional bases in quasi-Banach spaces with applications to Hardy spaces. II
• Banach spaces with a unique unconditional basis
• Uniqueness of unconditional basis of l_p(c₀) and l_p(l₂), 0<p<1
• Convexity conditions for non-locally convex lattices
• Banach spaces with a unique unconditional basis, up to permutation
• Orlicz sequence spaces without local convexity

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