On some additive mappings in rings with involution.
On a certain identitiy satisfied by a derivation and an arbitrary additive mapping. (Summary).
On a certain identity satisfied by a derivation and an arbitrary additive mapping.
The range of a derivation on a Jordan-Banach algebra
The questions when a derivation on a Jordan-Banach algebra has quasi-nilpotent values, and when it has the range in the radical, are discussed.
Maps preserving zero products
A linear map T from a Banach algebra A into another B preserves zero products if T(a)T(b) = 0 whenever a,b ∈ A are such that ab = 0. This paper is mainly concerned with the question of whether every continuous linear surjective map T: A → B that preserves zero products is a weighted homomorphism. We show that this is indeed the case for a large class of Banach algebras which includes group algebras. Our method involves continuous bilinear maps ϕ: A × A → X (for some Banach space X) with the property...
Lie triple ideals and Lie triple epimorphisms on Jordan and Jordan-Banach algebras
A linear subspace M of a Jordan algebra J is said to be a Lie triple ideal of J if [M,J,J] ⊆ M, where [·,·,·] denotes the associator. We show that every Lie triple ideal M of a nondegenerate Jordan algebra J is either contained in the center of J or contains the nonzero Lie triple ideal [U,J,J], where U is the ideal of J generated by [M,M,M]. Let H be a Jordan algebra, let J be a prime nondegenerate Jordan algebra with extended centroid C and unital central closure Ĵ, and let...
On a certain functional identity in prime rings. II.
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