Uniqueness of unconditional bases in quasi-Banach spaces with applications to Hardy spaces. II
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Publication:1355264
DOI10.1007/BF02774040zbMath0874.46007OpenAlexW2013939424MaRDI QIDQ1355264
Publication date: 11 November 1997
Published in: Israel Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02774040
Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) (46A16) Banach algebras of differentiable or analytic functions, (H^p)-spaces (46J15) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15)
Related Items (17)
Uniqueness of unconditional basis of infinite direct sums of quasi-Banach spaces ⋮ Fundamental functions of almost greedy bases of \(L_p\) for \(1<p< \infty\) ⋮ Uniqueness of unconditional basis of \(H_p(\mathbb{T}) \oplus \ell_2\) and \(H_p(\mathbb{T}) \oplus \mathcal{T}^{(2)}\) for \(0 < p < 1\) ⋮ 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 ⋮ Uniqueness of unconditional basis in quasi-Banach spaces which are not sufficiently Euclidean ⋮ Quasi-greedy bases in \(\ell_p\) (\(0 < p < 1\)) are democratic ⋮ On certain subspaces of \(\ell_p\) for \(0 < p \le 1\) and their applications to conditional quasi-greedy bases in \(p\)-Banach spaces ⋮ On a `philosophical' question about Banach envelopes ⋮ 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 bases in 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 ⋮ Subsequences of the Haar basis consisting of full levels in $H{\textunderscore }p$ for $0 < p < \infty $
Cites Work
- Uniqueness of unconditional bases in quasi-Banach spaces with applications to Hardy spaces
- Uniqueness of unconditional bases in Banach spaces
- The Mackey Topology and Complemented Subspaces of Lorentz Sequence Spaces d(w, p) for 0 < p < 1
- $H_{p}$-spaces, p≤1, and spline systems
- Convexity conditions for non-locally convex lattices
- Banach spaces with a unique unconditional basis, up to permutation
- Orlicz sequence spaces without local convexity
- Fréchet spaces with a unique unconditional basis
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