On the spectrum of a morphism of quotient Hilbert spaces.
Sobczyk's theorem and the Bounded Approximation Property
Sobczyk's theorem asserts that every c₀-valued operator defined on a separable Banach space can be extended to every separable superspace. This paper is devoted to obtaining the most general vector valued version of the theorem, extending and completing previous results of Rosenthal, Johnson-Oikhberg and Cabello. Our approach is homological and nonlinear, transforming the problem of extension of operators into the problem of approximating z-linear maps by linear maps.
Spectral mapping framework
In this paper we suggest a general framework of the spectral mapping theorem in terms of parametrized Banach space bicomplexes.
Splitting maps and norm bounds for the cyclic cohomology of biflat Banach algebras
We revisit the old result that biflat Banach algebras have the same cyclic cohomology as C, and obtain a quantitative variant (which is needed in separate, joint work of the author on the simplicial and cyclic cohomology of band semigroup algebras). Our approach does not rely on the Connes-Tsygan exact sequence, but is motivated strongly by its construction as found in [2] and [5].
Stably flat completions of universal enveloping algebras [Book]
The existence of critical values in an abstract perturbation problem.
The homology of spaces of simple topological measures
The simple topological measures X* on a q-space X are shown to be a superextension of X. Properties inherited from superextensions to topological measures are presented. The homology groups of various subsets of X* are calculated. For a q-space X, X* is shown to be a q-space. The homology of X* when X is the annulus is calculated. The homology of X* when X is a more general genus one space is investigated. In particular, X* for the torus is shown to have a retract homeomorphic to an infinite product...
The projective limit functor for spectra of webbed spaces
We study Palamodov's derived projective limit functor Proj¹ for projective spectra consisting of webbed locally convex spaces introduced by Wilde. This class contains almost all locally convex spaces appearing in analysis. We provide a natural characterization for the vanishing of Proj¹ which generalizes and unifies results of Palamodov and Retakh for spectra of Fréchet and (LB)-spaces. We thus obtain a general tool for solving surjectivity problems in analysis.
The structure of a subclass of amenable Banach algebras.
The structure of Lindenstrauss-Pełczyński spaces
Lindenstrauss-Pełczyński (for short ℒ) spaces were introduced by these authors [Studia Math. 174 (2006)] as those Banach spaces X such that every operator from a subspace of c₀ into X can be extended to the whole c₀. Here we obtain the following structure theorem: a separable Banach space X is an ℒ-space if and only if every subspace of c₀ is placed in X in a unique position, up to automorphisms of X. This, in combination with a result of Kalton [New York J. Math. 13 (2007)], provides a negative...
The topological snake lemma and corona algebras.
Weak homological bidimension and its values in the class of biflat Banach algebras.