Antisymmetry and analytic structure in the spectrum of a uniform Frechet algebra.
Application des ultraproduits à l'étude des espaces et des algèbres de Banach
Applications of harmonic functional calculus in a quotient involutive Banach algebra. (Applications du calcul fonctionnel harmonique dans une algèbre de Banach involutive quotient.)
Applications of the scarcity theorem in ordered Banach algebras
We apply Aupetit's scarcity theorem to obtain stronger versions of many spectral-theoretical results in ordered Banach algebras in which the algebra cone has generating properties.
Applying the density theorem for derivations to range inclusion problems
The problem of when derivations (and their powers) have the range in the Jacobson radical is considered. The proofs are based on the density theorem for derivations.
Approximate amenability for Banach sequence algebras
We consider when certain Banach sequence algebras A on the set ℕ are approximately amenable. Some general results are obtained, and we resolve the special cases where for 1 ≤ p < ∞, showing that these algebras are not approximately amenable. The same result holds for the weighted algebras .
Approximate amenability of semigroup algebras and Segal algebras [Book]
Approximate and weak amenability of certain Banach algebras
The notions of approximate amenability and weak amenability in Banach algebras are formally stronger than that of approximate weak amenability. We demonstrate an example confirming that approximate weak amenability is indeed actually weaker than either approximate or weak amenability themselves. As a consequence, we examine the (failure of) approximate amenability for -sums of finite-dimensional normed algebras.
Approximate biflatness and Johnson pseudo-contractibility of some Banach algebras
We study the structure of Lipschitz algebras under the notions of approximate biflatness and Johnson pseudo-contractibility. We show that for a compact metric space , the Lipschitz algebras and are approximately biflat if and only if is finite, provided that . We give a necessary and sufficient condition that a vector-valued Lipschitz algebras is Johnson pseudo-contractible. We also show that some triangular Banach algebras are not approximately biflat.
Approximate point joint spectra and multiplicative functionals
Approximate weak amenability, derivations and Arens regularity of Segal algebras
We continue our study of derivations, multipliers, weak amenability and Arens regularity of Segal algebras on locally compact groups. We also answer two questions on Arens regularity of the Lebesgue-Fourier algebra left open in our earlier work.
Approximately partial ternary quadratic derivations on Banach ternary algebras.
Arens regularity and local reflexivity principle for Banach algebras.
Arens Regularity of K (X).
Arens regularity of module actions
We study the Arens regularity of module actions of Banach left or right modules over Banach algebras. We prove that if has a brai (blai), then the right (left) module action of on * is Arens regular if and only if is reflexive. We find that Arens regularity is implied by the factorization of * or ** when is a left or a right ideal in **. The Arens regularity and strong irregularity of are related to those of the module actions of on the nth dual of . Banach algebras for which Z( **) = but are...
Arens Semi-Regular Banach Algebras.
Arens-regularity of algebras arising from tensor norms.
Aspects of the theory of derivations
We survey some old and new results in the theory of derivations on Banach algebras. Although our overview is broad ranging, our principal interest is in recent results concerning conditions on a derivation implying that its range is contained in the radical of the algebra.
Asymmetric decompositions of vectors in -algebras
By investigating the extent to which variation in the coefficients of a convex combination of unitaries in a unital -algebra permits that combination to be expressed as convex combination of fewer unitaries of the same algebra, we generalise various results of R. V. Kadison and G. K. Pedersen. In the sequel, we shall give a couple of characterisations of -algebras of .
Automatic continuity of biorthogonality preservers between weakly compact JB*-triples and atomic JBW*-triples
We prove that every biorthogonality preserving linear surjection from a weakly compact JB*-triple containing no infinite-dimensional rank-one summands onto another JB*-triple is automatically continuous. We also show that every biorthogonality preserving linear surjection between atomic JBW*-triples containing no infinite-dimensional rank-one summands is automatically continuous. Consequently, two atomic JBW*-triples containing no rank-one summands are isomorphic if and only if there exists a (not...