María Burgos

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.

Local triple derivations on C*-algebras and JB*-triples

In a first result we prove that every continuous local triple derivation on a JB

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

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Local Triple Derivations on C*-Algebras†

-triple is a triple derivation. We also give an automatic continuity result, that is, we show that local triple derivations on a JB

On mappings preserving zero products

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Banach spaces whose algebras of operators have a large group of unitary elements

-triple are continuous even if not assumed a priori to be so. In particular every local triple derivation on a C

Linear maps between C*-algebras that are *-homomorphisms at a fixed point

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Minus partial order and linear preservers

-algebra is a triple derivation. We also explore the connections between (bounded local) triple derivations and generalised (Jordan) derivations on a C

Determining Jordan (triple) homomorphisms by invertibility preserving conditions

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Linear maps preserving Fredholm and Atkinson elements of C *-algebras

-algebra.