  This work presents a parametrized family of divergences, namely Alpha-Beta
Log- Determinant (Log-Det) divergences, between positive definite unitized
trace class operators on a Hilbert space. This is a generalization of the
Alpha-Beta Log-Determinant divergences between symmetric, positive definite
matrices to the infinite-dimensional setting. The family of Alpha-Beta Log-Det
divergences is highly general and contains many divergences as special cases,
including the recently formulated infinite dimensional affine-invariant
Riemannian distance and the infinite-dimensional Alpha Log-Det divergences
between positive definite unitized trace class operators. In particular, it
includes a parametrized family of metrics between positive definite trace class
operators, with the affine-invariant Riemannian distance and the square root of
the symmetric Stein divergence being special cases. For the Alpha-Beta Log-Det
divergences between covariance operators on a Reproducing Kernel Hilbert Space
(RKHS), we obtain closed form formulas via the corresponding Gram matrices.
