Biorthogonal systems and big quotient spaces. (English) Zbl 0684.46016

Banach space theory, Proc. Res. Workshop, Iowa City/Iowa 1987, Contemp. Math. 85, 87-110 (1989).
[For the entire collection see Zbl 0669.00012.]
It is shown that every Banach space which has a quotient space not linearly injectable into \(\ell^{\infty}(A)\) contains a biorthogonal system of cardinality \(K>| A|\). The converse holds if X has property (\({\mathcal C})\) of Corson (i.e., every family of convex closed bounded sets with empty intersection contains a countable subfamily with empty intersection). This yields a quite complete description of biorthogonal systems in weak-star analytic subspaces of \(\ell^{\infty}(N)\) and finds an application in renormings of Banach spaces.
Reviewer: J.Szulga


46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
46B20 Geometry and structure of normed linear spaces


Zbl 0669.00012