A Kadison–sakai-Type Theorem

Mirzavaziri, Madjid; Moslehian, Mohammad Sal

doi:10.1017/s0004972708001160

Cited by 4 publications

(2 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One of the important questions in the theory of derivations is that "When are all bounded derivations on a Banach algebra inner?" Forty years ago, R. V. Kadison [3] and S. Sakai [10] independently proved that every derivation on a von Neumann algebra M is inner; see also [8]. Let σ : A → A be a homomorphism.…”

Section: Introductionmentioning

confidence: 99%

Innerness of higher derivations

Mirzavaziri¹,

Naranjani²,

Niknam³

2010

Banach J. Math. Anal.

View full text Add to dashboard Cite

Let A be an algebra. A sequence {d n } of linear mappings on A is called a higher derivation iffor each a, b ∈ A and each nonnegative integer n. In this paper a notion of an inner higher derivation is given. We characterize all uniformly bounded inner higher derivations on Banach algebras and show that each uniformly bounded higher derivation on a Banach algebra A is inner provided that each derivation on A is inner.

show abstract

Section: Introductionmentioning

confidence: 99%

Innerness of higher derivations

Mirzavaziri¹,

Naranjani²,

Niknam³

2010

Banach J. Math. Anal.

View full text Add to dashboard Cite

show abstract

“…For other approaches to generalized derivations and their applications see [1,2,3,11] and references therein. In particular, the automatic continuity problem for (σ, τ )-derivations is considered in [8,9,10] and an achievement of continuity of (σ, τ )-derivations without linearity is given in [5].…”

Section: Introductionmentioning

confidence: 99%

Ultraweak Continuity of σ-derivations on von Neumann Algebras

Mirzavaziri

Moslehian

2009

Math Phys Anal Geom

Self Cite

View full text Add to dashboard Cite

Suppose that A is an algebra, σ, τ : A → A are two linear mappings such that both σ(A) and τ (A) are subalgebras of A and X is aStudying some general algebraic aspects of (σ, τ )-derivations, we investigate the relation between amenability and (σ, τ )-amenability of Banach algebras in the case when σ, τ are homomorphisms. We prove that if A is a C * -algebra and σ, τ are * -homomorphisms with ker(σ) = ker(τ ), then A is (σ, τ )-amenable if and only if σ(A) is amenable.2000 Mathematics Subject Classification. Primary 46H25; Secondary 47B47, 46L05.

show abstract

(σ, τ)-amenability of C*-algebras

Mirzavaziri

Moslehian

2011

GMJ

View full text Add to dashboard Cite

Suppose that is an algebra, σ, τ : → are two linear mappings such that both σ() and τ() are subalgebras of and 𝒳 is a (τ(), σ())-bimodule. A linear mapping D : → 𝒳 is called a (σ, τ)-derivation if D(ab) = D(a) · σ(b) + τ(a) · D(b) (a, b ∈ ). A (σ, τ)-derivation D is called a (σ, τ)-inner derivation if there exists an x ∈ 𝒳 such that D is of the form either or . A Banach algebra is called (σ, τ)-amenable if every (σ, τ)-derivation from into a dual Banach (τ(), σ())-bimodule is (σ, τ)-inner. Studying some general algebraic aspects of (σ, τ)-derivations, we investigate the relation between the amenability and the (σ, τ)-amenability of Banach algebras in the case where σ, τ are homomorphisms. We prove that if 𝔄 is a C*-algebra and σ, τ are *-homomorphisms with ker(σ) = ker(τ), then 𝔄 is (σ, τ)-amenable if and only if σ(𝔄) is amenable.

show abstract

A Kadison–sakai-Type Theorem

Cited by 4 publications

References 8 publications

Innerness of higher derivations

Innerness of higher derivations

Ultraweak Continuity of σ-derivations on von Neumann Algebras

(σ, τ)-amenability of C*-algebras

Contact Info

Product

Resources

About