Hilbert–Carleman determinant

In functional analysis, the Hilbert–Carleman determinant is an operator determinant for certain integral operators on Banach spaces, whose kernels are not necessarily continuous. Unlike Fredholm determinant which is generally not defined for integral operators whose kernels are discontinuous on the diagonal, the Hilbert–Carleman determinant can be defined even when this condition fails. Similarly to the Fredholm determinant, the Hilbert–Carleman determinant is defined for sums of the form ${\displaystyle I+A}$ where ${\displaystyle I}$ is the identity operator and ${\displaystyle A}$ is an integral operator.

The Hilbert–Carleman determinant is named after David Hilbert and Torsten Carleman.