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3 Studia Mathematica

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On isomorphisms of standard operator algebras

100%

Molnár L.

2000

tom 142

nr 3

295-302

We show that between standard operator algebras every bijective map with a certain multiplicativity property related to Jordan triple isomorphisms of associative rings is automatically additive.

Non-linear Jordan triple automorphisms of sets of self-adjoint matrices and operators

100%

Molnár L.

nr 1

39-48

We consider the so-called Jordan triple automorphisms of some important sets of self-adjoint operators without the assumption of linearity. These transformations are bijective maps which satisfy the equality ϕ(ABA) = ϕ(A)ϕ(B)ϕ(A) on their domains. We determine the general forms of these maps (under the assumption of continuity) on the sets of all invertible positive operators, of all positive operators, and of all invertible self-adjoint operators.

A metric on the space of projections admitting nice isometries

63%

Molnár L. , Timmermann W.

nr 3

271-281

Motivated by the concept of separation between propositions in quantum logic, we introduce the so-called separation metric or Santos metric on the space of all projections in a Hilbert space. We show that the resulting metric space has only "nice" surjective isometries. On the nontrivial projections they are all unitarily or antiunitarily equivalent to the identity or to taking the orthogonal complement. We relate this result to Wigner's classical theorem on the form of quantum mechanical symmetry transformations.