Dual Banach algebras and Connes-amenability.
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 results of factorization for operators.
Duality and Lorentz-Marcinkiewicz operator spaces.
Duality in the theory of crossed products.
Duality of measures of non-𝒜-compactness
Let be a Banach operator ideal. Based on the notion of -compactness in a Banach space due to Carl and Stephani, we deal with the notion of measure of non–compactness of an operator. We consider a map (respectively, ) acting on the operators of the surjective (respectively, injective) hull of such that (respectively, ) if and only if the operator T is -compact (respectively, injectively -compact). Under certain conditions on the ideal , we prove an equivalence inequality involving and ....
Dunford-Pettis-like properties of continuous vector function spaces.
operators between normed spaces
Each operator in L (lp,lr) (1 ≤ r < p < ∞) is compact.
It is known that each bounded operator from lp → lris compact. The purpose of this paper is to present a very simple proof of this useful fact.
Eigenvalues of Integral Operators. II.
Eine Charakterisierung der Boole'schen Algebra zu einer ...-direkten Zerlegung.
Embedding C(K) in B(X).
Embeddings of finite-dimensional operator spaces into the second dual
We show that, if a a finite-dimensional operator space E is such that X contains E C-completely isomorphically whenever X** contains E completely isometrically, then E is -completely isomorphic to Rₘ ⊕ Cₙ for some n, m ∈ ℕ ∪ 0. The converse is also true: if X** contains Rₘ ⊕ Cₙ λ-completely isomorphically, then X contains Rₘ ⊕ Cₙ (2λ + ε)-completely isomorphically for any ε > 0.
Entropy and Eigenvalues of Certain Integral Operators.
Entropy and n-widths of operators in Banach spaces
Entropy considerations in the noncommutative setting.
Entropy numbers of r-nuclear operators between spaces
Equivalences involving (p,q)-multi-norms
We consider (p,q)-multi-norms and standard t-multi-norms based on Banach spaces of the form , and resolve some question about the mutual equivalence of two such multi-norms. We introduce a new multi-norm, called the [p,q]-concave multi-norm, and relate it to the standard t-multi-norm.
Equivariant KK-theory for semimultiplicative sets.
Ergodic actions of compact groups on operator algebras. III. Classification for SU (2).