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Partially defined σ-derivations on semisimple Banach algebras

Tsiu-Kwen Lee, Cheng-Kai Liu (2009)

Studia Mathematica

Let A be a semisimple Banach algebra with a linear automorphism σ and let δ: I → A be a σ-derivation, where I is an ideal of A. Then Φ(δ)(I ∩ σ(I)) = 0, where Φ(δ) is the separating space of δ. As a consequence, if I is an essential ideal then the σ-derivation δ is closable. In a prime C*-algebra, we show that every σ-derivation defined on a nonzero ideal is continuous. Finally, any linear map on a prime semisimple Banach algebra with nontrivial idempotents is continuous if it satisfies the σ-derivation...

Problems concerning n -weak amenability of a Banach algebra

Alireza Medghalchi, Taher Yazdanpanah (2005)

Czechoslovak Mathematical Journal

In this paper we extend the notion of n -weak amenability of a Banach algebra 𝒜 when n . Technical calculations show that when 𝒜 is Arens regular or an ideal in 𝒜 * * , then 𝒜 * is an 𝒜 ( 2 n ) -module and this idea leads to a number of interesting results on Banach algebras. We then extend the concept of n -weak amenability to n .

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