On the strong lacunary convergence and strong Cesàro summability of sequences of real-valued functions.
On the strong McShane integral of functions with values in a Banach space
The classical Bochner integral is compared with the McShane concept of integration based on Riemann type integral sums. It turns out that the Bochner integrable functions form a proper subclass of the set of functions which are McShane integrable provided the Banach space to which the values of functions belong is infinite-dimensional. The Bochner integrable functions are characterized by using gauge techniques. The situation is different in the case of finite-dimensional valued vector functions....
On the structural theory of factors of negatively curved groups
Ozawa showed in [21] that for any i.c.c. hyperbolic group, the associated group factor is solid. Developing a new approach that combines some methods of Peterson [29], Ozawa and Popa [27, 28], and Ozawa [25], we strengthen this result by showing that is strongly solid. Using our methods in cooperation with a cocycle superrigidity result of Ioana [12], we show that profinite actions of lattices in , , are virtually -superrigid.
On the structure of -algebras of type .
On the structure of a vector measure.
On the structure of Banach spaces with an unconditional basic sequence
For a Banach space X with an unconditional basic sequence, one of the following regular-irregular alternatives holds: either X contains a subspace isomorphic to ℓ₂, or X contains a subspace which has an unconditional finite-dimensional decomposition, but does not admit such a decomposition with a uniform bound for the dimensions of the decomposition. This result can be viewed in the context of Gowers' dichotomy theorem.
On the structure of Banach spaces with Mazur's intersection property.
On the structure of certain ultradistributions.
On the structure of compact subsets of ℂₚ
On the structure of covers of sofic shifts.
On the structure of derivations on certain nonamenable nuclear Banach algebras.
On the structure of fixed point sets of some compact maps in the Fréchet space
The aim of this note is 1. to show that some results (concerning the structure of the solution set of equations (18) and (21)) obtained by Czarnowski and Pruszko in [6] can be proved in a rather different way making use of a simle generalization of a theorem proved by Vidossich in [8]; and 2. to use a slight modification of the “main theorem” of Aronszajn from [1] applying methods analogous to the above mentioned idea of Vidossich to prove the fact that the solution set of the equation (24), (25)...
On the structure of G-spaces
On the structure of Jordan *-derivations
On the structure of Mellin distributions
On the structure of non-dentable subsets of
It is shown that there is no closed convex bounded non-dentable subset K of such that on subsets of K the PCP and the RNP are equivalent properties. Then applying the Schachermayer-Rosenthal theorem, we conclude that every non-dentable K contains a non-dentable subset L so that on L the weak topology coincides with the norm topology. It follows from known results that the RNP and the KMP are equivalent on subsets of .
On the Structure of Non-Weakly Compact Operators on Banach Lattices.
On the structure of rank one elements in Banach algebras.
On the structure of separable spaces (1 < p < ∞)
On the structure of support point sets.