Continuous Jordan triple endomorphisms of P2\mathbb{P}_2

We describe the structure of all continuous Jordan triple endomorphisms of the set $\mathbb{P}_2$ of all positive definite $2\times 2$ matrices thus completing a recent result of ours. We also mention an application concerning sorts of surjective generalized isometries on $\mathbb{P}_2$ and, as second application, we complete another former result of ours on the structure of sequential endomorphisms of finite dimensional effect algebras

Fidelity preserving maps on density operators

We prove that any bijective fidelity preserving transformation on the set of all density operators on a Hilbert space is implemented by an either unitary or antiunitary operator on the underlying Hilbert space.Comment: This is corrected version of the paper math.OA/0108060. The paper has already appeared in ROMP (vol. 48 (2001), 299-303

A generalization of Wigner's unitary-antiunitary theorem to Hilbert modules

Let H be a Hilbert $C^*$-module over a matrix algebra A. It is proved that any function $T:H\to H$ which preserves the absolute value of the (generalized) inner product is of the form $Tf=\phi(f)Uf$ $(f\in H)$, where $\phi$ is a phase-function and U is an A-linear isometry. The result gives a natural extension of Wigner's classical unitary-antiunitary theorem for Hilbert modules.Comment: 27 pages. To appear in J. Math. Phy

General Mazur-Ulam type theorems and some applications

Recently we have presented several structural results on certain isometries of spaces of positive definite matrices and on those of unitary groups. The aim of this paper is to put those previous results into a common perspective and extend them to the context of operator algebras, namely, to that of von Neumann factors

Bilocal automorphisms

We prove that every bilocal automorphism of a matrix algebra is either an inner automorphism, or an inner anti-automorphism, or it is of a very special degenerate form. Bijective continuous bilocal automorphisms of a unital standard operator algebra on an in�nite-dimensional separable complex Banach space are automorphisms

Algebraic reflexivity of isometry groups and automorphism groups of some operator structures

We establish the algebraic re exivity of three isometry groups of operator structures: The group of all surjective isometries on the unitary group, the group of all surjective isometries on the set of all positive invertible operators equipped with the Thompson metric, and the group of all surjective isometries on the general linear group of B(H), the operator algebra over a complex infinite dimensional separable Hilbert space H. We show that those isometry groups coincide with certain groups of automorphisms of corresponding structures and hence we also obtain the re exivity of some automorphism groups