Bi-squeezed states arising from pseudo-bosons

Extending our previous analysis on bi-coherent states, we introduce here a new class of quantum mechanical vectors, the bi-squeezed states, and we deduce their main mathematical properties. We relate bi-squeezed states to the so-called regular and non regular pseudo-bosons. We show that these two cases are different, from a mathematical point of view. Some physical examples are considered. (paper)