quasireflexive

Of a relation ~ on a set S: such that every element that is related to some element is also related to itself, i.e. ∀x,y∈S: x~y ⇒ x~x ∧ y~y.

Of a Banach space X: such that the quotient X ′′ / J(X) has finite dimension d. (It is then said to be "quasireflexive of order d".)