Jorge J. Garcés

ORTHOGONALITY PRESERVERS REVISITED

We obtain a complete characterization of all orthogonality preserving operators from a JB*-algebra to a JB*-triple. If T : J → E is a bounded linear operator from a JB*-algebra (respectively, a C*-algebra) to a JB*-triple and h denotes the element T**(1), then T is orthogonality preserving, if and only if, T preserves zero-triple-products, if and only if, there exists a Jordan *-homomorphism such that S(x) and h operator commute and T(x) = h•r(h) S(x), for every x ∈ J, where r(h) is the range tripotent of h, is the Peirce-2 subspace associated to r(h) and •r(h) is the natural product making a JB*-algebra. This characterization culminates the description of all orthogonality preserving operators between C*-algebras and JB*-algebras and generalizes all the previously known results in this line of study.

A Kowalski–Słodkowski theorem for 2-local \(^*\)-homomorphisms on von Neumann algebras

It is established that every (not necessarily linear) 2-local

Orthogonally Additive and Orthogonality Preserving Holomorphic Mappings between C*-Algebras

^*

Generalised Triple Homomorphisms and Derivations

∗-homomorphism from a von Neumann algebra into a C

Orthogonality preservers in C∗-algebras, JB∗-algebras and JB∗-triples☆

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Automatic continuity of biorthogonality preservers between compact C⁎-algebras and von Neumann algebras☆

∗-algebra is linear and a