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Approximate amenability for Banach sequence algebras

H. G. Dales, R. J. Loy, Y. Zhang (2006)

Studia Mathematica

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 A = ℓ p for 1 ≤ p < ∞, showing that these algebras are not approximately amenable. The same result holds for the weighted algebras ℓ p ( ω ) .

Approximate and weak amenability of certain Banach algebras

P. Bharucha, R. J. Loy (2010)

Studia Mathematica

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 ℓ p -sums of finite-dimensional normed algebras.

Approximate biflatness and Johnson pseudo-contractibility of some Banach algebras

Amir Sahami, Mohammad R. Omidi, Eghbal Ghaderi, Hamzeh Zangeneh (2020)

Commentationes Mathematicae Universitatis Carolinae

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 X , the Lipschitz algebras Lip α ( X ) and lip α ( X ) are approximately biflat if and only if X is finite, provided that 0 < α < 1 . 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.

Arens regularity of module actions

M. Eshaghi Gordji, M. Filali (2007)

Studia Mathematica

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 ( n ) of . Banach algebras for which Z( **) = but ⊊ Z t ( * * ) are...

Aspects of the theory of derivations

Gerard Murphy (1994)

Banach Center Publications

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 J B * -algebras

Akhlaq A. Siddiqui (2006)

Archivum Mathematicum

By investigating the extent to which variation in the coefficients of a convex combination of unitaries in a unital J B * -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 J B * -algebras of t s r 1 .

Automatic continuity of biorthogonality preservers between weakly compact JB*-triples and atomic JBW*-triples

María Burgos, Jorge J. Garcés, Antonio M. Peralta (2011)

Studia Mathematica

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...

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