摘要：In this contribution we construct noncommutative transposition hypergroups of integral operators on spaces of continuous functions which are determined by Fredholm
integral equations of the first and second kinds. We started with integral operators
formed by separated kernel. Moreover, we investigate the obtained hyperstructures as
transposition hypergroups and also related quasi-hypergroups of blocks of equivalence of
integral operators. Moreover, we use also the object function (where the corresponding
binary hyperoperation on an ordered group is defined as principal end generated by products of pairs of elements of the considered group) of a functor enabling the transfer
from the category of ordered groups and their isotone homomorphisms into the category
of hypergroups and their inclusion homomorphisms.
The basic group of integral operators contains an invariant subgroup. Using another
binary operation on the set of suitable Fredholm integral operators of the second kind
we get a group with a significant non-invariant subgroup of operators of the first kind
enabling the construction of a quasi-hypergroup of decomposition classes of operators,
structure of which is also clarified.
