Gamow vectors and time asymmetry

We prove that Gamow vectors are important tools in the quantum theory of ir reversibility. We use the mathematical formalism of rigged Hilbert spaces. We discuss some spectral formulas that include Gamow vectors as well as som e results concerning Gamow vectors. The role of the time-reversal operator is studied. The formalism can be applied to formulate a sense of irreversib ility in cosmology.