Lajos Molnár

Some characterizations of the automorphisms of () and ()

We present some nonlinear characterizations of the automorphisms of the operator algebra B(H) and the function algebra C(X) by means of their spectrum preserving properties.

Some linear preserver problems on upper triangular matrices

We consider linear preserver problems on the algebra of upper triangular matrices. We obtain the general form of nonsingular linear maps preserving rank one idempotents or commutativity. We give examples to show that the nonsingularity assumption is essential in our results.

Order-automorphisms of the set of bounded observables

Let H be a complex Hilbert space and denote by Bs(H) the set of all self-adjoint bounded linear operators on H. In this article we describe the form of all bijective maps (no linearity or continuity is assumed) on Bs(H) which preserve the order ⩽ in both directions.

Local automorphisms of operator algebras on Banach spaces

In this paper we extend a result of Semrl stating that every 2-local automorphism of the full operator algebra on a separable infinite dimensional Hilbert space is an automorphism. In fact, besides separable Hilbert spaces, we obtain the same conclusion for the much larger class of Banach spaces with Schauder bases. The proof rests on an analogous statement concerning the 2-local automorphisms of matrix algebras for which we present a short proof. The need to get such a proof was formulated in Semrls paper.

A condition for a subspace of B(H) to be an ideal

Abstract Let H be a real or complex Hilbert space with dim H > 1. The subspace A ⊂ B (H) is an ideal if and only if TA − AT∗ ∈ A for every T ∈ B (H) , A ∈ A . Every element of B (H) is the finite sum of TA − AT∗ type operators.

An algebraic approach to Wigner's unitary-antiunitary theorem

We present an operator algebraic approach to Wigners unitary-antiunitary theorem using some classical results from ring theory. To show how effective this approach is, we prove a generalization of this celebrated theorem for Hilbert modules over matrix algebras. We also present a Wigner-type result for maps on prime C *-algebras.

Thompson isometries of the space of invertible positive operators

We determine the structure of bijective isometries of the set of all invertible positive operators on a Hilbert space equipped with the Thompson metric or the Hilbert projective metric.

Transformations on the Set of All n-Dimensional Subspaces of a Hilbert Space Preserving Principal Angles

Abstract: Wigners classical theorem on symmetry transformations plays a fundamental role in quantum mechanics. It can be formulated, for example, in the following way: Every bijective transformation on the set ℒ of all 1-dimensional subspaces of a Hilbert space H which preserves the angle between the elements of ℒ is induced by either a unitary or an antiunitary operator on H. The aim of this paper is to extend Wigners result from the 1-dimensional case to the case of n-dimensional subspaces of H with n∈ℕ fixed.

Characterizations of the Automorphisms of Hilbert Space Effect Algebras

Abstract: In this paper we characterize the automorphisms of Hilbert space effect algebras by means of their preserving properties which concern certain relations and quantities appearing in quantum measurement theory.

Maps on states preserving the relative entropy

Let H be a finite dimensional Hilbert space. The aim of this short note is to prove that every bijective map on the space S(H) of all density operators on H which preserves the relative entropy is of the form ϕ(ρ)=UρU* with some unitary or antiunitary operator U on H.