Removability of ideals in commutative Banach algebras
We develop a theory of removable singularities for the weighted Bergman space , where is a Radon measure on . The set is weakly removable for if , and strongly removable for if . The general theory developed is in many ways similar to the theory of removable singularities for Hardy spaces, and locally Lipschitz spaces of analytic functions, including the existence of counterexamples to many plausible properties, e.g. the union of two compact removable singularities needs not be removable....
The aim of this paper is to show that for every Banach space (X, || · ||) containing asymptotically isometric copy of the space c0 there is a bounded, closed and convex set C ⊂ X with the Chebyshev radius r(C) = 1 such that for every k ≥ 1 there exists a k-contractive mapping T : C → C with [...] for any x ∊ C.
It is a well-known fact that genetic sequences may contain sections with repeated units, called repeats, that differ in length over a population, with a length distribution of geometric type. A simple class of recombination models with single crossovers is analysed that result in equilibrium distributions of this type. Due to the nonlinear and infinite-dimensional nature of these models, their analysis requires some nontrivial tools from measure theory and functional analysis, which makes them interesting...
This note is to report some of the advances obtained as a follow-up of the book [2] on the topic of twisted sums of Banach spaces. Since this announcement is no longer enough to contain the theory being developed, we submit the interested reader to [2] and to [1], where full details and proofs shall appear.
It is proved that a representable non-separable Banach space does not admit uniformly Gâteaux-smooth norms. This is true in particular for C(K) spaces where K is a separable non-metrizable Rosenthal compact space.