The semigroup of Fredholm operators.
The signature package on Witt spaces
In this paper we prove a variety of results about the signature operator on Witt spaces. First, we give a parametrix construction for the signature operator on any compact, oriented, stratified pseudomanifold which satisfies the Witt condition. This construction, which is inductive over the ‘depth’ of the singularity, is then used to show that the signature operator is essentially self-adjoint and has discrete spectrum of finite multiplicity, so that its index—the analytic signature of —is well-defined....
The simultaneous existence of linear functionals
The space of all bounded operators on Hilbert space does not have the approximation property
The space Weak H¹
The spatial flatness and injectiveness of Connes operator algebras.
The Stability of the Euler Characteristic for Hilbert Complexes.
The stable range of C*-algebras.
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 symmetric tensor product of a direct sum of locally convex spaces
An explicit representation of the n-fold symmetric tensor product (equipped with a natural topology τ such as the projective, injective or inductive one) of the finite direct sum of locally convex spaces is presented. The formula for gives a direct proof of a recent result of Díaz and Dineen (and generalizes it to other topologies τ) that the n-fold projective symmetric and the n-fold projective “full” tensor product of a locally convex space E are isomorphic if E is isomorphic to its square .
The Taylor spectrum and quotient Banach spaces
The tensor product of a locally pseudo-convex and a nuclear space
The topological snake lemma and corona algebras.
The universal Banach space with a -suppression unconditional basis
Using the technique of Fraïssé theory, for every constant , we construct a universal object in the class of Banach spaces possessing a normalized -suppression unconditional Schauder basis.
The universal right K-property for some interpolation spaces
The -approximation property and the weak topology in tensor products of Banach spaces
There is no cogenerator of totally convex spaces
Topological algebras of kernels.
Topological localization in Fréchet algebras.