T. Y. Lam proposed abstracting algebraic properties of the Peirce
corners eRe associated with an idempotent e in a ring R and introduced the
notion of general corners. We consider this notion principally in the
context of C*-algebras and some operator spaces in place of a ring R. Our
aim is to characterise such corners as fully as we can, ideally by
establishing that they are related to the ranges of the more well-known
completely positive conditional expectations.