  By a quantum speed limit one usually understands an estimate on how fast a
quantum system can evolve between two distinguishable states. The most known
quantum speed limit is given in the form of the celebrated Mandelstam-Tamm
inequality that bounds the speed of the evolution of a state in terms of its
energy dispersion. In contrast to the basic Mandelstam-Tamm inequality, we are
concerned not with a single state but with a (possibly infinite-dimensional)
subspace which is subject to the Schroedinger evolution. By using the concept
of maximal angle between subspaces we derive optimal bounds on the speed of
such a subspace evolution. These bounds may be viewed as further
generalizations of the Mandelstam-Tamm inequality. Our study includes the case
of unbounded Hamiltonians.
