The aliasing-norm formula for consistent sampling from oblique decompositions

Let $\mathcal{H}$ be an arbitrary Hilbert space and let $\mathcal{S}\oplus\mathcal{T}^{\perp}=\mathcal{H}$ be an oblique decomposition. Consider the consistent sampling problem associated with this decomposition, and let $A(\mathcal{S},\mathcal{T})$ denote its aliasing norm. The preceding proposition asserts, for the shift-invariant setting, that the aliasing norm is given by the tangent of the corresponding angle between the subspaces.

Aliasing-norm conjecture. The formula in Proposition should hold for the consistent sampling corresponding to the oblique decomposition

$$\mathcal{S}\oplus\mathcal{T}^{\perp}=\mathcal{H}$$

in an arbitrary Hilbert space $\mathcal{H}$.

The conjecture is known for finite-dimensional $\mathcal{S}$ and $\mathcal{T}$, and the proposition establishes it for some infinite-dimensional subspaces as well. Its validity for arbitrary Hilbert spaces and oblique decompositions remains open.