On the connection between real and complex interpolation of quasi-Banach spaces
The authors generalize the formula (which is known for Banach couples) \[ [(A_0,A_1)_{\theta_0,q_0}, (A_0,A_1)_{\theta_1,q_1}]_\lambda= (A_0,A_1) _{\theta,q} \] to the case of quasi--Banach couples \((A_0,A_1)\). There are some earlier results to this question and the authors introduce a new approach to handle such spaces which works also in end--point cases. This gives (Theorem 5) the mapping of the right space to the left one above for \(0<\theta_0,\theta_1,\lambda<1,\;0<q_0,q_1<\infty\) or \(0<q_0<\infty\) and \(q_1=\infty\) (putting \(\theta=(1-\lambda)\theta_0+\lambda \theta_1,\;\frac {1} {q}=\frac {1-\lambda} {q_0}+\frac {\lambda} {q_1}\)). The other direction (Theorem 3) needs some technical condition on the couple \((A_0,A_1)\). Theorems 6 and 4 give corresponding results for end--point cases. Applications are given to function spaces and Schatten classes.
scientific article; zbMATH DE number 1138709
scientific article