منابع مشابه
HIGHER POINT DERIVATIONS ON COMMUTATIVE BANACH ALGEBRAS, III fey
i=o hold for each choice of / and g in A and k in { 1 , . . . , q}. A point derivation of infinite order is an infinite sequence {dk} of linear functional such that (1.1) holds for all k. A point derivation is continuous if each dk is continuous, totally discontinuous if dk is discontinuous for each fcSl, and degenerate if d1 = 0. Some of the terminology given in the previous paragraph was intr...
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In [2] Singer and Wermer showed that a bounded derivation in a commutative Banach algebra 21 necessarily maps 21 into the radical 91. They conjectured at this time that the assumption of boundedness could be dropped. It is a corollary of results proved below that if 21 is in addition regular and semi-simple, this is indeed the case. What is actually proved here is that under the above hypothese...
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Given a von Neumann algebra M with a faithful normal semi-finite trace τ, we consider the non commutative Arens algebra Lω(M, τ) = ⋂ p≥1 Lp(M, τ) and the related algebras L2 (M, τ) = ⋂ p≥2 Lp(M, τ) and M + L2 (M, τ) which are proved to be complete metrizable locally convex *-algebras. The main purpose of the present paper is to prove that any derivation of the algebra M + L2 (M, τ) is inner and...
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It is well known that the (solvable) radical of a Lie or Jordan algebra is invariant under all derivations of the algebra if the groundfield is not modular [4] and [5]. In this note we obtain a similar result for commutative power-associative algebras of degree one by following Jacobson's argument in [5] and then appealing to a theorem of Gerstenhaber [3] at that point where the Jordan identity...
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We characterize derivations and 2-local derivations from Mn(A) into Mn(M), n ≥ 2, where A is a unital algebra over C and M is a unital A-bimodule. We show that every derivation D : Mn(A) → Mn(M), n ≥ 2, is the sum of an inner derivation and a derivation induced by a derivation from A to M. We say that A commutes with M if am = ma for every a ∈ A and m ∈ M. If A commutes with M we prove that eve...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1976
ISSN: 0040-8735
DOI: 10.2748/tmj/1178240744