3 research outputs found
Orthogonal forms and orthogonality preservers on real function algebras
We initiate the study of orthogonal forms on a real C-algebra. Motivated
by previous contributions, due to Ylinen, Jajte, Paszkiewicz and Goldstein, we
prove that for every continuous orthogonal form on a commutative real
C-algebra, , there exist functionals and in
satisfying for every
in . We describe the general form of a (not-necessarily continuous)
orthogonality preserving linear map between unital commutative real
C-algebras. As a consequence, we show that every orthogonality preserving
linear bijection between unital commutative real C-algebras is continuous.Comment: To appear in Linear and Multilinear Algebr
Local triple derivations on C*-algebras
We prove that every bounded local triple derivation on a unital C*-algebra is
a triple derivation. A similar statement is established in the category of
unital JB*-algebras.Comment: 12 pages, submitte
2-local triple homomorphisms on von Neumann algebras and JBW-triples
We prove that every (not necessarily linear nor continuous) 2-local triple
homomorphism from a JBW-triple into a JB-triple is linear and a triple
homomorphism. Consequently, every 2-local triple homomorphism from a von
Neumann algebra (respectively, from a JBW-algebra) into a C-algebra
(respectively, into a JB-algebra) is linear and a triple homomorphism