THE PEETRE K-METHOD IN STRONG $\lambda$-K-MONOTONE SPACES

THE PEETRE K-METHOD IN STRONG $\lambda$-K-MONOTONE SPACES

In [5], M. Cwikel and J. Peetre showed that some Banach couples are Calderon pairs and every K-monotone cones in that couples can be constructed by the Peetre K-method. With the help of theorem 4 in [3], we can extend the above result to the K-monotone spaces. In [4], M. Cwikel provided the proof of therem 4 in [3] and also mentioned that some theorems in [5] which were stated in terms of K-monotone cones can be extended to K-monotone spaces. But M. Cwikel and J.Peetre's results only cover the case when over bar A = over bar B. We extend this result to the case when over bar A.neq. over bar B. In this case, we need a condition stronger than that the K-monotone space.