Distinguished subspaces of of maximal dimension
Distortion and spreading models in modified mixed Tsirelson spaces
The results of the first part concern the existence of higher order ℓ₁ spreading models in asymptotic ℓ₁ Banach spaces. We sketch the proof of the fact that the mixed Tsirelson space T[(ₙ,θₙ)ₙ], and , admits an spreading model in every block subspace. We also prove that if X is a Banach space with a basis, with the property that there exists a sequence (θₙ)ₙ ⊂ (0,1) with , such that, for every n ∈ ℕ, for every ₙ-admissible block sequence of vectors in X, then there exists c > 0 such...
Divergent vector sequences {yₙ} with Δyₙ → 0
An approximation property of divergent sequences in normed vector spaces is discussed.
Does C* -embedding imply C*-embedding in the realm of products with a non-discrete metric factor?
The above question was raised by Teodor Przymusiński in May, 1983, in an unpublished manuscript of his. Later on, it was recognized by Takao Hoshina as a question that is of fundamental importance in the theory of rectangular normality. The present paper provides a complete affirmative solution. The technique developed for the purpose allows one to answer also another question of Przymusiński's.
Does Kirk's theorem hold for multivalued nonexpansive mappings?
Domains of ...-Holomorphy in a Separable Banach Space.
Domains of partial attraction in several dimensions
Domination and equivalence of sequences of subspaces in dual spaces
Domination by positive Banach-Saks operators
Given a positive Banach-Saks operator T between two Banach lattices E and F, we give sufficient conditions on E and F in order to ensure that every positive operator dominated by T is Banach-Saks. A counterexample is also given when these conditions are dropped. Moreover, we deduce a characterization of the Banach-Saks property in Banach lattices in terms of disjointness.
Domination of operators in the non-commutative setting
We consider majorization problems in the non-commutative setting. More specifically, suppose E and F are ordered normed spaces (not necessarily lattices), and 0 ≤ T ≤ S in B(E,F). If S belongs to a certain ideal (for instance, the ideal of compact or Dunford-Pettis operators), does it follow that T belongs to that ideal as well? We concentrate on the case when E and F are C*-algebras, preduals of von Neumann algebras, or non-commutative function spaces. In particular, we show that, for C*-algebras...
Double-dual -types over Banach spaces not containing .
Double-dual types over the Banach space .
DP1 and completely continuous operators.
Drop property equals reflexivity
Dual Banach algebras: representations and injectivity
We study representations of Banach algebras on reflexive Banach spaces. Algebras which admit such representations which are bounded below seem to be a good generalisation of Arens regular Banach algebras; this class includes dual Banach algebras as defined by Runde, but also all group algebras, and all discrete (weakly cancellative) semigroup algebras. Such algebras also behave in a similar way to C*- and W*-algebras; we show that interpolation space techniques can be used in place of GNS type arguments....
Dual properties for unconditionally converging operators
Dual renormings of Banach spaces
We prove that a Banach space admitting an equivalent WUR norm is an Asplund space. Some related dual renormings are also presented.
Dual results of factorization for operators.
Dual spaces generated by the interior of the set of norm attaining functionals
We characterize some isomorphic properties of Banach spaces in terms of the set of norm attaining functionals. The main result states that a Banach space is reflexive as soon as it does not contain ℓ₁ and the dual unit ball is the w*-closure of the convex hull of elements contained in the "uniform" interior of the set of norm attaining functionals. By assuming a very weak isometric condition (lack of roughness) instead of not containing ℓ₁, we also obtain a similar result. As a consequence of the...
Dual spaces of compact operator spaces and the weak Radon-Nikodým property
We deal with the weak Radon-Nikodým property in connection with the dual space of (X,Y), the space of compact operators from a Banach space X to a Banach space Y. First, under the weak Radon-Nikodým property, we give a representation of that dual. Next, using this representation, we provide some applications to the dual spaces of (X,Y) and , the space of weak*-weakly continuous operators.