We work with the weighted poly-Bergman spaces defined on the unit disk, which are subspaces of the weighted \(L^2\) space over the same domain. Particularly, we take interest in the extended Fock space formalism theory applied to this case and generalize some of the second author’s results from the standard to the weighted case. Using properties of the elements of an orthonormal basis for the weighted \(L^2\) space, comprising orthogonal polynomials referred to as disk polynomials, we express a variety of operators, including pure isometries, in a basis-independent manner, hence completing a description to the extended Fock space corresponding to the ladder operators defined on the space.
