  A large literature specifies conditions under which the information
complexity for a sequence of numerical problems defined for dimensions $1, 2,
\ldots$ grows at a moderate rate, i.e., the sequence of problems is tractable.
Here, we focus on the situation where the space of available information
consists of all linear functionals and the problems are defined as linear
operator mappings between Hilbert spaces. We unify the proofs of known
tractability results and generalize a number of existing results. These
generalizations are expressed as five theorems that provide equivalent
conditions for (strong) tractability in terms of sums of functions of the
singular values of the solution operators.
