Three space properties and basis extensions

DOI10.1007/BF02764003zbMath0921.46010MaRDI QIDQ1275682

Wolfgang Lusky

Publication date: 13 June 1999

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

zbMATH Keywords

subspacequotient space\({\mathcal L}_{\infty}\)-space\({\mathcal L}_{1}\)-spacebasis extension

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Classical Banach spaces in the general theory (46B25) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15)

Related Items (8)

Approximation in Müntz spaces \(M_{\Lambda,p}\) of \(L_p\) functions for \(1<p<\infty\) and bases ⋮ Approximation and existence of Schauder bases in Müntz spaces of \(L_{1}\) functions ⋮ Schauder bases in Dirac modules over quaternions ⋮ Isomorphic classification of reflexive Müntz spaces ⋮ On the bounded approximation property in Banach spaces ⋮ Some approximation properties of Banach spaces and Banach lattices ⋮ Bilinear forms and the \(\mathrm{Ext}^2\)-problem in Banach spaces ⋮ On the bounded approximation property on subspaces of \(\ell_p\) when \(0 < p < 1\) and related issues

Cites Work

• A note on Banach spaces containing \(c_ 0\) or \(C_{\infty}\)
• A Banach space without a basis which has the bounded approximation property
• The \(L_ p\) spaces
• On bases, finite dimensional decompositions and weaker structures in Banach spaces
• A counterexample to the approximation problem in Banach spaces
• On bases and unconditional convergence of series in Banach spaces
• Bases, lacunary sequences and complemented subspaces in the spaces $L_{p}$
• Universal bases
• Any separable Banach space with the bounded approximation property is a complemented subspace of a Banach space with a basic

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