STRUCTURE THEOREM FOR -OPERATORS

In this paper we prove a structure theorem for the class of $\mathcal{AN}$-operators between separable, complex Hilbert spaces which is similar to that of the singular value decomposition of a compact operator. Apart from this, we show that a bounded operator is $\mathcal{AN}$ if and only if it is either compact or a sum of a compact operator and scalar multiple of an isometry satisfying some condition. We obtain characterizations of these operators as a consequence of this structure theorem and deduce several properties which are similar to those of compact operators.