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Let E be a Banach space with a separable dual. Zippin’s theorem asserts that E embeds in a Banach space with a shrinking basis, and W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński have shown that E is a quotient of a Banach space with a shrinking basis. These two results use the interpolation theorem established by W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński. Here, we prove that the Szlenk indices of and can be controlled by the Szlenk index of E, where the Szlenk index...
Let f be a function in the Douglas algebra A and let I be a finitely generated ideal in A. We give an estimate for the distance from f to I that allows us to generalize a result obtained by Bourgain for to arbitrary Douglas algebras.
The notion of non-orthogonal multi-resolution analysis and its compatibility with differentiation (as expressed by the commutation formula) lead us to the construction of a multi-resolution analysis of L2(Rn)n which is well adapted to the approximation of divergence-free vector functions. Thus, we obtain unconditional bases of compactly supported divergence-free vector wavelets.
Let be a Banach space with a countable unconditional basis (e.g., ),
an open set and complex-valued holomorphic functions
on , such that the Fréchet differentials are linearly
independant over at each . We suppose that
is a complete intersection and we consider a
holomorphic Banach vector bundle . If (resp.) denote the ideal of
germs of holomorphic functions on that vanish on (resp. the sheaf of germs
of holomorphic sections of ), then the sheaf cohomology groups ,
vanish...
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