Maps on the $n$-dimensional subspaces of a Hilbert space preserving principal angles

Transformations on the set of all n-dimensional subspaces of a Hilbert space preserving principal angles

Wigner’s 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 ...

ORTHOGONALITY PRESERVING TRANSFORMATIONS ON THE SET OF n-DIMENSIONAL SUBSPACES OF A HILBERT SPACE

We characterize bijective transformations on the set of all n-dimensional subspaces of a Hilbert space that preserve orthogonality in both directions. This extends Uhlhorn’s improvement of Wigner’s classical theorem on symmetry transformations.

On Principal Angles between Subspaces of Euclidean Space

A Note on Quadratic Maps for Hilbert Space Operators

In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...  

Comparability preserving maps on Hilbert space effect algebras

We describe the general form of bijective comparability preserving transformations of the Hilbert space effect algebra, thus improving several known characterizations of ortho-order automorphisms.