Derivations in Prime Rings

Abstract. The first section of the paper deals with linear operators T i : U −→ V , i = 1, . . . , n, where U and V are vector spaces over an infinite field, such that for every u ∈ U , the vectors T 1 u, . . . , Tnu are linearly dependent modulo a fixed finite dimensional subspace of V . In the second section, outer derivations of dense algebras of linear operators are discussed. The results of the first two sections of the paper are applied in the last section, where commuting pairs of continuous derivations d, g of a Banach algebra A such that (dg)(x) is quasi-nilpotent for every x ∈ A are characterized.

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“…This contradiction proves (3). In order to see that the inequality (3) is sharp we consider a vector space V = V 1 ⊕ V 0 with dim V 1 = n − 1.…”

Section: Locally Linearly Dependent Operatorsmentioning

confidence: 97%

On locally linearly dependent operators and derivations

Brešar

Šemrl

1999

Trans. Amer. Math. Soc.

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“…In [13], Bergen initiated the study of semiderivations from R into itself with the extra condition that δσ = σ δ. The characterization of semiderivations of a prime ring was given by Brešar [14] and Chuang [15] independently.…”

Section: Definition Let σ Be An Endomorphism Of R An Additive Map δ mentioning

confidence: 99%