2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72889We 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.Updated, a new section on history and physical meaning of quasi-states added. To appear in Comment. Math. HelvSymplectic GeometryFunctional AnalysisQuantum Physicstext