Operators, Spaces, Algebras, Modules 2010

Generalized bicircular projections on JB*-triples

Let $\mathcal{X}$ be a complex Banach space. Let $P : \mathcal{X} \to \mathcal{X}$ be a linear projection, that is a linear mapping with the property $P^2=P,$ and let $\overline{P}$ denote its complementary projection $I-P,$ where $I$ is the identity operator on $\mathcal{X}.$ A projection $P$ is called a generalized bicircular projection if the mapping $P + \lambda \overline{P}$ is an isometry for some modulus one complex number $\lambda \neq 1.$ The aim of this talk is to describe the structure of these mappings on JB*-triples, in particular C*-algebras, as well as $S(\mathcal{H})$ and $A(\mathcal{H}),$ the linear subspace of all symmetric operators on a complex Hilbert space $\mathcal{H},$ and the linear subspace of all antisymmetric operators on $\mathcal{H},$ respectively.