  A left ideal of any $C^*$-algebra is an example of an operator algebra with a
right contractive approximate identity (r.c.a.i.). Indeed left ideals in
$C^*$-algebras may be characterized as the class of such operator algebras,
which happen also to be triple systems.
  Conversely, we show here and in a sequel to this paper, that operator
algebras with r.c.a.i. should be studied in terms of a certain left ideal of a
$C^*$-algebra. We study left ideals from the perspective of `Hamana theory' and
using the multiplier algebras introduced by the author. More generally, we
develop some general theory for operator algebras which have a 1-sided identity
or approximate identity, including a Banach-Stone theorem for these algebras,
and an analysis of the `multiplier operator algebra'.
