Uniqueness of unconditional bases in nonlocally convex \(c_0\)-products

DOI10.1007/S11856-011-0060-2zbMath1261.46002OpenAlexW2054310608MaRDI QIDQ1758901

Fernando Albiac, Camino Leránoz

Publication date: 19 November 2012

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11856-011-0060-2

zbMATH Keywords

uniqueness of unconditional basis up to permutationnatural quasi-Banach spacestrongly absolute unconditional basis

Mathematics Subject Classification ID

Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) (46A16) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Summability and bases in topological vector spaces (46A35)

Related Items (4)

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 \(0 < p < 1\) ⋮ Uniqueness of unconditional bases in nonlocally convex \(\ell _{1}\)-products ⋮ On the permutative equivalence of squares of unconditional bases

Cites Work

• Uniqueness of unconditional bases in nonlocally convex \(\ell _{1}\)-products
• 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
• Uniqueness of the unconditional basis of \(\ell_{1}(\ell_p)\) and \(\ell_p(\ell_1)\), \(0<p<1\)
• Banach spaces with a unique unconditional basis
• 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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