  We provide examples for negativity of structure constants of the stably
canonical basis of modified quantum $\mathfrak{gl}_n$ and an analogous basis of
modified quantum coideal algebra of $\mathfrak{gl}_n$. In contrast, we
construct the canonical basis of the modified quantum coideal algebra of
$\mathfrak{sl}_n$, establish the positivity of its structure constants, the
positivity with respect to a geometric bilinear form as well as the positivity
of its action on the tensor powers of the natural representation. The matrix
coefficients of the transfer map on these Schur algebras with respect to the
canonical bases are shown to be positive. Formulas for canonical basis of the
iSchur algebra of rank one are obtained.
