  We establish a link between symplectic topology and a recently emerged branch
of functional analysis called the theory of quasi-states and quasi-measures. In
the symplectic context quasi-states can be viewed as an algebraic way of
packaging certain information contained in Floer theory, and in particular in
spectral invariants of Hamiltonian diffeomorphisms introduced recently by
Yong-Geun Oh. As a consequence we prove a number of new results on rigidity of
intersections in symplectic manifolds. This work is a part of a joint project
with Paul Biran.
