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We establish representation theorems in terms of finite rank operators for some operator ideals defined by approximation numbers. We also study the stability under tensor product of these ideals.

We show a direct proof for the generalized Hardy’s inequality obtained by the first author Math. Nachr. 126, 281-300, 1986. Our techniques are elementary and work in the limit case which was not… (More)

The authors prove a representation theorem in terms of finite rank operators for operators´T on Banach spaces which satisfy sup n2N (log n) an(T) < 1, 0 < < 1.
Here an(T) denote the approximation… (More)