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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 homological properties of Banach algebras associated with locally compact groups

Mehdi Nemati (2015)

Colloquium Mathematicae

We investigate some homological notions of Banach algebras. In particular, for a locally compact group G we characterize the most important properties of G in terms of some homological properties of certain Banach algebras related to this group. Finally, we use these results to study generalized biflatness and biprojectivity of certain products of Segal algebras on G.

Some module cohomological properties of Banach algebras

Elham Ilka, Amin Mahmoodi, Abasalt Bodaghi (2020)

Mathematica Bohemica

We find some relations between module biprojectivity and module biflatness of Banach algebras 𝒜 and ℬ and their projective tensor product 𝒜 ⊗ ^ ℬ . For some semigroups S , we study module biprojectivity and module biflatness of semigroup algebras l 1 ( S ) .

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.

Some remarks on Q -algebras

Nicolas Th. Varopoulos (1972)

Annales de l'institut Fourier

We study Banach algebras that are quotients of uniform algebras and we show in particular that the class is stable by interpolation. We also show that ℓ p , ( 1 ≤ p ≤ ∞ ) are Q algebras and that A n = ℨ L 1 ( Z ; 1 + | n | α ) is a Q -algebra if and only if α > 1 / 2 .

Some simple proofs in holomorphic spectral theory

Graham R. Allan (2007)

Banach Center Publications

This paper gives some very elementary proofs of results of Aupetit, Ransford and others on the variation of the spectral radius of a holomorphic family of elements in a Banach algebra. There is also some brief discussion of a notorious unsolved problem in automatic continuity theory.

Spaces of multipliers and their preduals for the order multiplication on [0, 1]

Savita Bhatnagar, H. L. Vasudeva (2002)

Colloquium Mathematicae

Let I = [0, 1] be the compact topological semigroup with max multiplication and usual topology. C(I), L p ( I ) , 1 ≤ p ≤ ∞, are the associated Banach algebras. The aim of the paper is to characterise H o m C ( I ) ( L r ( I ) , L p ( I ) ) and their preduals.

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