Approximation numbers for relatively bounded operators

Abstract

Let T be a densely defined closed operator between Banach spaces X and Y. Aconcept of approximation
numbers, called T–approximation numbers, is considered for T–bounded operators between Banach
spaces X and Z with their domains contained in X, and some properties of such T–approximation numbers
are studied. The theorems proved in the paper include a result on approximation of T–approximation numbers
of a T–bounded operator A using T–approximation numbers of An, where fAng is a certain sequence
of operators which converges to A in some sense. This result is analogous to a theorem proved recently by
the authors in [3] for bounded linear operators.