Subspace Perturbation

Question

For two positive semidefinite matrices $A,B\in\mathbb{R}^{n\times n}$, with dominant $r$ dimensional subspaces $U,V\in\mathbb{R}^{n\times r}$ and eigenvalues $\Sigma_A, \Sigma_B$, what can we say about the singular values of the matrix $$ \left(U\Sigma_A^{1/2}\right)^TV\Sigma_B^{1/2} = \Sigma_A^{1/2}U^TV\Sigma_B^{1/2} $$ in terms of $\|A-B\|_{op}$ or $\|A-B\|_F$ ?