  The current work generalizes the author's previous work on the
infinite-dimensional Alpha Log-Determinant (Log-Det) divergences and Alpha-Beta
Log-Det divergences, defined on the set of positive definite unitized trace
class operators on a Hilbert space, to the entire Hilbert manifold of positive
definite unitized Hilbert-Schmidt operators. This generalization is carried out
via the introduction of the extended Hilbert-Carleman determinant for unitized
Hilbert-Schmidt operators, in addition to the previously introduced extended
Fredholm determinant for unitized trace class operators. The resulting
parametrized family of Alpha-Beta Log-Det divergences is general and contains
many divergences between positive definite unitized Hilbert-Schmidt operators
as special cases, including the infinite-dimensional affine-invariant
Riemannian distance and the infinite-dimensional generalization of the
symmetric Stein divergence.
