I was wondering if there is an analogue to the classical Riesz Thorin theorem for Schatten classes. I suppose the answer is yes, since Schatten classes are so similar to $\ell^p$ spaces for which the theorem holds. However, I could not find a reference online. In particular, does one have to take the bounded or compact operators as the infinity space when interpolating?- I suppose bounded ones as they are the dual of the trace-class operators which fits to $(L^1 )'=L^{\infty}.$
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