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Character contractibility of Banach algebras and homological properties of Banach modules

100%

Nasr-Isfahani R., Soltani Renani S.

Studia Mathematica

2011

tom 202

nr 3

205-225

Let 𝓐 be a Banach algebra and let ϕ be a nonzero character on 𝓐. We give some necessary and sufficient conditions for the left ϕ-contractibility of 𝓐 as well as several hereditary properties. We also study relations between homological properties of some Banach left 𝓐-modules, the left ϕ-contractibility and the right ϕ-amenability of 𝓐. Finally, we characterize the left character contractibility of various Banach algebras related to locally compact groups.

Vector-valued invariant means on spaces of bounded linear maps

81%

Dashti M., Nasr-Isfahani R., Soltani Renani S.

Colloquium Mathematicum

2013

tom 132

nr 1

1-11

Let 𝓐 be a Banach algebra and let ℳ be a W*-algebra. For a homomorphism Φ from 𝓐 into ℳ, we introduce and study ℳ -valued invariant Φ-means on the space of bounded linear maps from 𝓐 into ℳ. We establish several characterizations of existence of an ℳ -valued invariant Φ-mean on B(𝓐,ℳ). We also study the relation between existence of an ℳ -valued invariant Φ-mean on B(𝓐,ℳ) and amenability of 𝓐. Finally, for a character ϕ of 𝓐, we give some descriptions for ϕ-amenability of 𝓐 in terms of ℳ -valued invariant Φ-means.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Studia Mathematica

2 Nasr-Isfahani R.

2 Soltani Renani S.

1 Dashti M.

1 2013

1 2011

Wyniki wyszukiwania

Character contractibility of Banach algebras and homological properties of Banach modules

Vector-valued invariant means on spaces of bounded linear maps