  One of the fundamental physical limits on the speed of time evolution of a
quantum state is known in the form of the celebrated Mandelstam-Tamm
inequality. This inequality gives an answer to the question on how fast an
isolated quantum system can evolve from its initial state to an orthogonal one.
In its turn, the Fleming bound is an extension of the Mandelstam-Tamm
inequality that gives an optimal speed bound for the evolution between
non-orthogonal initial and final states. In the present work, we are concerned
not with a single state but with a whole (possibly infinite-dimensional)
subspace of the system states that are subject to the Schroedinger evolution.
By using the concept of maximal angle between subspaces we derive an optimal
estimate on the speed of such a subspace evolution that may be viewed as a
natural generalization of the Fleming bound.
