  In this paper we draw attention to the fact that the studies by V. G.
Kadyshevsky devoted to the creation of the which \emph{\emph{to the geometric
quantum field theory with a fundamental mass}} containing non-Hermitian mass
extensions. It is important that these ideas recently received a powerful
development in the form of construction of the non-Hermitian algebraic
approach. The central point of these theories is the construction of new scalar
products in which the average values of non-Hermitian Hamiltonians are valid.
Among numerous works on this subject may be to allocate as purely mathematical
and containing a discussion of experimental results. In this regard, we
consider as the development of algebraic relativistic pseudo-Hermitian quantum
theory with a maximal mass and experimentally significant investigations are
discussed
