  We work with very general Banach spaces of analytic functions in the disk or
other domains which satisfy a minimum number of natural axioms. Among the
preliminary results, we discuss some implications of the basic axioms and
identify all functional Banach spaces in which every bounded analytic function
is a pointwise multiplier. Next, we characterize (in various ways) the weighted
composition operators among the bounded operators on such spaces, thus
generalizing some well-known results on multiplication or composition
operators. We also characterize the invertible weighted composition operators
on the disk and on general Banach spaces of analytic functions on bounded
domains under different sets of axioms whose connections we discuss by
providing appropriate examples. This generalizes and complements various recent
results by Gunatillake, Bourdon, and Hyv\"arinen-Lindstr\"om-Nieminen-Saukko.
