Division Rings and Group von Neumann Algebras.
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The above question was raised by Teodor Przymusiński in May, 1983, in an unpublished manuscript of his.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 Dirichlet forms and effective resistance estimates on p.c.f. fractals
We consider post-critically finite self-similar fractals with regular harmonic structures. We first obtain effective resistance estimates in terms of the Euclidean metric, which in particular imply the embedding theorem for the domains of the Dirichlet forms associated with the harmonic structures. We then characterize the domains of the Dirichlet forms.
Domains of ...-Holomorphy in a Separable Banach Space.
Domains of integral operators
It is shown that the proper domains of integral operators have separating duals but in general they are not locally convex. Banach function spaces which can occur as proper domains are characterized. Some known and some new results are given, illustrating the usefulness of the notion of proper domain.
Domains of partial attraction in several dimensions
Domains which are locally uniformly linearly convex in the Kobayashi distance.
Dominated ergodic theorems in rearrangement invariant spaces
We study conditions under which Dominated Ergodic Theorems hold in rearrangement invariant spaces. Consequences for Orlicz and Lorentz spaces are given. In particular, our results generalize the classical theorems for the spaces and the classes .
Dominated operators on C[0, 1] and the (CRP).
We show that a B-space E has the (CRP) if and only if any dominated operator T from C[0, 1] into E is compact. Hence we apply this result to prove that c0 embeds isomorphically into the B-space of all compact operators from C[0, 1] into an arbitrary B-space E without the (CRP).
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 in Analysis
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...
Domination properties in ordered Banach algebras
We recall from [9] the definition and properties of an algebra cone C of a real or complex Banach algebra A. It can be shown that C induces on A an ordering which is compatible with the algebraic structure of A. The Banach algebra A is then called an ordered Banach algebra. An important property that the algebra cone C may have is that of normality. If C is normal, then the order structure and the topology of A are reconciled in a certain way. Ordered Banach algebras have interesting spectral properties....
Double convergence and products of Fréchet spaces
The paper is devoted to convergence of double sequences and its application to products. In a convergence space we recognize three types of double convergences and points, respectively. We give examples and describe their structure and properties. We investigate the relationship between the topological and convergence closure product of two Fréchet spaces. In particular, we give a necessary and sufficient condition for the topological product of two compact Hausdorff Fréchet spaces to be a Fréchet...
Double exponential integrability, Bessel potentials and embedding theorems
This paper is a continuation of [5] and provides necessary and sufficient conditions for double exponential integrability of the Bessel potential of functions from suitable (generalized) Lorentz-Zygmund spaces. These results are used to establish embedding theorems for Bessel potential spaces which extend Trudinger's result.
Double multipliers on topological algebras.
Double Operator Integrals and Submajorization
We present a user-friendly version of a double operator integration theory which still retains a capacity for many useful applications. Using recent results from the latter theory applied in noncommutative geometry, we derive applications to analogues of the classical Heinz inequality, a simplified proof of a famous inequality of Birman-Koplienko-Solomyak and also to the Connes-Moscovici inequality. Our methods are sufficiently strong to treat these...
Double Sequence Spaces Definedby a Sequence of Modulus Functions over -normed Spaces
In the present paper we introduce some double sequence spaces defined by a sequence of modulus function over -normed spaces. We also make an effort to study some topological properties and inclusion relations between these spaces.