Abstract. We study biorthogonal sequences with special properties, such as weak or weak-star convergence to 0, and obtain an extension of the Josefson-Nissenzweig theorem.This result is applied to embed analytic disks in the fiber over 0 of the spectrum of H ∞ (B), the algebra of bounded analytic functions on the unit ball B of an arbitrary infinite dimensional Banach space. Various other embedding theorems are obtained. For instance, if the Banach space is superreflexive, then the unit ball of a Hilbert spac…
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