This very interesting paper develops a general machinery for establishing double centralizer properties for several classes of associative algebras. In other words, this gives some sufficient conditions for a finite-dimensional associative algebra, \(A\), to coincide with the so-called double centralizer algebra \(\text{End}(M_{\text{End}_A(M)})\) for some \(M\in A\)-mod. The classical part of this theory, developed by H. Tachikawa [Quasi-Frobenius rings and generalizations. Lect. Notes Math. 351, Springer, Berlin (1973; Zbl 0271.16004)], guarantees the existence of the double centralizer property for algebras of dominant dimension at least two with respect to a faithful projective-injective module. In the paper under review the authors extend this result to quasi-hereditary algebras of dominant dimension at least two with respect to some (not necessarily full) tilting module. As an outcome a rather short and free from technicalities proof for Soergel’s double centralizer theorem [W. Soergel, J. Am. Math. Soc. 3, 421-445 (1990; Zbl 0747.17008)], relating category \(\mathcal O\) with the coinvariant algebra, is given and a generalization of this theorem on certain parabolic analogues for \(\mathcal O\) is obtained. Both results use only a short list of easy properties of \(\mathcal O\) and do not require any invariant theory. Moreover, the authors also reprove the classical Schur-Weyl duality theorem for Schur algebras \(S_k(n,r)\) as well as the corresponding result for quantized Schur algebras \(S_q(n,r)\). The case \(n\geq r\) is handled using Tachikawa’s results, whereas the case \(n<r\) already requires the corresponding generalization for tilting modules.