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Segal algebras, approximate identities and norm irregularity in C₀(X,A)

Jussi Mattas (2013)

Studia Mathematica

We study three closely related concepts in the context of the Banach algebra C₀(X,A). We show that, to a certain extent, Segal extensions, norm irregularity and the existence of approximate identities in C₀(X,A) can be deduced from the corresponding features of A and vice versa. Extensive use is made of the multiplier norm and the tensor product representation of C₀(X,A).

Small deformations of topological algebras

Mati Abel, Krzysztof Jarosz (2003)

Studia Mathematica

We investigate stability of various classes of topological algebras and individual algebras under small deformations of multiplication.

Some algebraic and homological properties of Lipschitz algebras and their second duals

F. Abtahi, E. Byabani, A. Rejali (2019)

Archivum Mathematicum

Let ( X , d ) be a metric space and α > 0 . We study homological properties and different types of amenability of Lipschitz algebras Lip α X and their second duals. Precisely, we first provide some basic properties of Lipschitz algebras, which are important for metric geometry to know how metric properties are reflected in simple properties of Lipschitz functions. Then we show that all of these properties are equivalent to either uniform discreteness or finiteness of X . Finally, some results concerning the character...

Some algebras without submultiplicative norms or positive functionals

Michael Meyer (1995)

Studia Mathematica

We prove a conjecture of Yood regarding the nonexistence of submultiplicative norms on the algebra C(T) of all continuous functions on a topological space T which admits an unbounded continuous function. We also exhibit a quotient of C(T) which does not admit a nonzero positive linear functional. Finally, it is shown that the algebra L(X) of all linear operators on an infinite-dimensional vector space X admits no nonzero submultiplicative seminorm.

Some notions of amenability for certain products of Banach algebras

Eghbal Ghaderi, Rasoul Nasr-Isfahani, Mehdi Nemati (2013)

Colloquium Mathematicae

For two Banach algebras and ℬ, an interesting product × θ ℬ , called the θ-Lau product, was recently introduced and studied for some nonzero characters θ on ℬ. Here, we characterize some notions of amenability as approximate amenability, essential amenability, n-weak amenability and cyclic amenability between and ℬ and their θ-Lau product.

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