Uniqueness of unconditional bases in Banach spaces

DOI10.1007/BF02762272zbMath0939.46009arXivmath/9610210MaRDI QIDQ1279632

Peter G. Casazza, Nigel J. Kalton

Publication date: 16 February 1999

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

Full work available at URL: https://arxiv.org/abs/math/9610210

zbMATH Keywords

Banach latticeTsirelson spaceBanach sequence spaceNakano spacecomplemented subspaces of Orlicz sequence spacescomplemented unconditional basic sequencesuniqueness of unconditional bases in finite-dimensional spaces

Mathematics Subject Classification ID

Banach lattices (46B42) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Banach sequence spaces (46B45)

Related Items (22)

Uniqueness of unconditional basis of infinite direct sums of quasi-Banach spaces ⋮ Some equivalence relations which are Borel reducible to isomorphism between separable Banach spaces ⋮ Fundamental functions of almost greedy bases of \(L_p\) for \(1<p< \infty\) ⋮ Uniqueness of unconditional bases in quasi-Banach spaces with applications to Hardy spaces. II ⋮ 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 ⋮ The ergodicity of weak Hilbert spaces ⋮ Disjointly Homogeneous Banach Lattices and Applications ⋮ 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 ⋮ Uniqueness of the unconditional basis of \(\ell_{1}(\ell_p)\) and \(\ell_p(\ell_1)\), \(0<p<1\) ⋮ On the number of permutatively inequivalent basic sequences in a Banach space ⋮ Uniqueness of unconditional basis in Lorentz sequence spaces ⋮ Disjointly homogeneous Banach lattices: duality and complementation ⋮ Banach spaces with a unique greedy basis ⋮ Addendum to: ``Uniqueness of unconditional basis of infinite direct sums of quasi-Banach spaces ⋮ On the permutative equivalence of squares of unconditional bases ⋮ Some types of convergence related to the reconstruction property in Banach spaces

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