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Dual complementors in topological algebras

Marina Haralampidou (2005)

Banach Center Publications

We deal with dual complementors on complemented topological (non-normed) algebras and give some characterizations of a dual pair of complementors for some classes of complemented topological algebras. The study of dual complementors shows their deep connection with dual algebras. In particular, we refer to Hausdorff annihilator locally C*-algebras and to proper Hausdorff orthocomplemented locally convex H*-algebras. These algebras admit, by their nature, the same type of dual pair of complementors....

Entire functions and equicontinuity of power maps in Baire algebras.

Abdellah El Kinani (2000)

Revista Matemática Complutense

We obtain that the power maps are equicontinuous at zero in any Baire locally convex algebra with a continuous product in which all entire functions operate; whence is m-convex in the commutative case. As a consequence, we get the same result of Mityagin, Rolewicz and Zelazko for commutative B0-algebras.

General construction of Banach-Grassmann algebras

Vladimir G. Pestov (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We show that a free graded commutative Banach algebra over a (purely odd) Banach space E is a Banach-Grassmann algebra in the sense of Jadczyk and Pilch if and only if E is infinite-dimensional. Thus, a large amount of new examples of separable Banach-Grassmann algebras arise in addition to the only one example previously known due to A. Rogers.

Generalization of the weak amenability on various Banach algebras

Madjid Eshaghi Gordji, Ali Jabbari, Abasalt Bodaghi (2019)

Mathematica Bohemica

The generalized notion of weak amenability, namely ( ϕ , ψ ) -weak amenability, where ϕ , ψ are continuous homomorphisms on a Banach algebra 𝒜 , was introduced by Bodaghi, Eshaghi Gordji and Medghalchi (2009). In this paper, the ( ϕ , ψ ) -weak amenability on the measure algebra M ( G ) , the group algebra L 1 ( G ) and the Segal algebra S 1 ( G ) , where G is a locally compact group, are studied. As a typical example, the ( ϕ , ψ ) -weak amenability of a special semigroup algebra is shown as well.

Higher-dimensional weak amenability

B. Johnson (1997)

Studia Mathematica

Bade, Curtis and Dales have introduced the idea of weak amenability. A commutative Banach algebra A is weakly amenable if there are no non-zero continuous derivations from A to A*. We extend this by defining an alternating n-derivation to be an alternating n-linear map from A to A* which is a derivation in each of its variables. Then we say that A is n-dimensionally weakly amenable if there are no non-zero continuous alternating n-derivations on A. Alternating n-derivations are the same as alternating...

Homology and cohomology of Rees semigroup algebras

Frédéric Gourdeau, Niels Grønbæk, Michael C. White (2011)

Studia Mathematica

Let S be a Rees semigroup, and let ℓ¹(S) be its convolution semigroup algebra. Using Morita equivalence we show that bounded Hochschild homology and cohomology of ℓ¹(S) are isomorphic to those of the underlying discrete group algebra.

Ideal amenability of module extensions of Banach algebras

Eshaghi M. Gordji, F. Habibian, B. Hayati (2007)

Archivum Mathematicum

Let 𝒜 be a Banach algebra. 𝒜 is called ideally amenable if for every closed ideal I of 𝒜 , the first cohomology group of 𝒜 with coefficients in I * is zero, i.e. H 1 ( 𝒜 , I * ) = { 0 } . Some examples show that ideal amenability is different from weak amenability and amenability. Also for n ∈ N , 𝒜 is called n -ideally amenable if for every closed ideal I of 𝒜 , H 1 ( 𝒜 , I ( n ) ) = { 0 } . In this paper we find the necessary and sufficient conditions for a module extension Banach algebra to be 2-ideally amenable.

Injective semigroup-algebras

J. Green (1998)

Studia Mathematica

Semigroups S for which the Banach algebra ℓ 1 ( S ) is injective are investigated and an application to the work of O. Yu. Aristov is described.

Local algebras and the largest spectrum finite ideal.

Antonio Fernández López, Omar Jaa (1998)

Extracta Mathematicae

M. R. F. Smyth proved in [9, Theorem 3.2] that the socle of a semiprimitive Banach complex algebra coincides with the largest algebraic ideal. Later M. Benslimane, A. Kaidi and O. Jaa showed [3] the equality between the socle and the largest spectrum finite ideal in semiprimitive alternative Banach complex algebras. In fact, they showed that every spectrum finite one-sided ideal of a semiprimitive alternative Banach complex algebra is contained in the socle. In this note a new proof is given of...

Locally m-pseudoconvex topologies on locally A-pseudoconvex algebras

M. Abel, J. Arhippainen (2004)

Czechoslovak Mathematical Journal

Let ( A , T ) be a locally A-pseudoconvex algebra over ℝ or ℂ . We define a new topology m ( T ) on A which is the weakest among all m-pseudoconvex topologies on A stronger than T . We describe a family of non-homogeneous seminorms on A which defines the topology m ( T ) .

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