Maps on positive operators preserving Lebesgue decompositions.
Thompson isometries on positive operators: the 2-dimensional case.
Bijectivity of *-Endomorphisms of ...(H) and the Unilateral Shift.
Jordan *-derivation pairs on a complex *-algebra. (Summary).
Kolmogorov-Smirnov isometries and affine automorphisms of spaces of distribution functions
In this paper we describe the structure of surjective isometries of the spaces of all absolutely continuous, singular, or discrete probability distribution functions on R equipped with the Kolmogorov-Smirnov metric. We also study the structure of affine automorphisms of the space of all distribution functions.
On isomorphisms of standard operator algebras
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.
The set of automorphisms of B(H) is topologically reflexive in B(B(H))
The aim of this paper is to prove the statement announced in the title which can be reformulated in the following way. Let H be a separable infinite-dimensional Hilbert space and let Φ: B(H) → B(H) be a continuous linear mapping with the property that for every A ∈ B(H) there exists a sequence of automorphisms of B(H) (depending on A) such that . Then Φ is an automorphism. Moreover, a similar statement holds for the set of all surjective isometries of B(H).
Non-linear Jordan triple automorphisms of sets of self-adjoint matrices and operators
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.
On the range of a normal Jordan -derivation
In this note, by means of the spectrum of the generating operator, we characterize the self-adjointness and closedness of the range of a normal and a self-adjoint Jordan *-derivation, respectively.
Modular bases in a Hilbert -module
Locally inner derivations of standard operator algebras
It is proved that every locally inner derivation on a symmetric norm ideal of operators is an inner derivation.
A metric on the space of projections admitting nice isometries
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...
Reflexivity of the isometry group of some classical spaces.
We investigate the reflexivity of the isometry group and the automorphism group of some important metric linear spaces and a1gebras. The paper consists of the following sections: 1. Preliminaries. 2. Sequence spaces. 3. Spaces of measurable functions. Hardy spaces. 5. Banach algebras of holomorphic functions. 6. Fréchet algebras of holomorphic functions. 7. Spaces of continuous functions.
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