The exactness of the projective limit functor on the category of quotients of Frechet spaces
We give conditions under which the functor projective limit is exact on the category of quotients of Fréchet spaces of L. Waelbroeck [18].
The existence of critical values in an abstract perturbation problem.
The functor σ²X
We disprove the existence of a universal object in several classes of spaces including the class of weakly Lindelöf Banach spaces.
The geometry of a closed form
It is proved that a closed r-form ω on a manifold M defines a cohomology (called ω-coeffective) on M. A general algebraic machinery is developed to extract some topological information contained in the ω-coeffective cohomology. The cases of 1-forms, symplectic forms, fundamental 2-forms on almost contact manifolds, fundamental 3-forms on -manifolds and fundamental 4-forms in quaternionic manifolds are discussed.
The Grothendieck property for injective tensor products of Banach spaces
The Hahn-Banach Theorem surveyed [Book]
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 ideal property of tensor products of Banach lattices with applications to the local structure of spaces of absolutely summing operators
The ideal structure of the Haagerup tensor product of C*-algebras.
The laplacian and the Dirac operator in infinitely many variables
The Lions's problem for Gustavsson-Peetre functor.
The problem of coincidence of the interpolation spaces obtained by use of the interpolation method of Gustavsson-Peetre generated by (parameters) quasi-concave functions is investigated. It is shown that a restriction of this method to the class of all non-trivial Banach couples gives different interpolation spaces whenever two different parameters satisfying some conditions are used.
The Mackey completions of some interpolation F-spaces
The Mayer-Vietoris and the Puppe sequences in K-theory for C*-algebras
The -field-irreducible part of a -point functional
The n-ball properties in real and complex Banach spaces.
The Poulsen simplex is not a tensor 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 projective tensor product of Fréchet-Montel spaces
The range of a contractive projection in Lp(H).
We show that the range of a contractive projection on a Lebesgue-Bochner space of Hilbert valued functions Lp(H) is isometric to a lp-direct sum of Hilbert-valued Lp-spaces. We explicit the structure of contractive projections. As a consequence for every 1 < p < ∞ the class Cp of lp-direct sums of Hilbert-valued Lp-spaces is axiomatizable (in the class of all Banach spaces).
The Schur multiplication in tensor algebras