  In this paper we define the Schwartz linear operators among spaces of
tempered distributions. These operators are the analogous of linear continuous
operators among separable Hilbert spaces, but in the case of spaces endowed
with Schwartz bases having a continuous index set. The Schwartz linear
operators enjoy properties very similar to those enjoyed by linear operators in
the finite dimensional case. The Schwartz operators are one possible rigorous
mathematical model for the operators and observables used in Quantum Mechanics.
