ON CERTAIN DENSELY INVARIANT QUANTITIES OF LINEAR-OPERATORS

Let L(X,Y) denote the class of linear transformations T : D(T) C X --> Y where X and Y are normed spaces. A quantity f is called densely inv ariant if for every system L(X, Y) and every operator T is an element of L(X,Y) we have f(T\E) = f(T) whenever E is a core of T. The density invariance of certain well known quantities is established. In case Y is complete and T is closable, a stronger property is shown to hold f or some of these quantitites, namely invariance under restriction to d ense subspaces.