Schatten class operator
In mathematics, specifically functional analysis, a pth Schatten-class operator is a bounded linear operator on a Hilbert space with finite pth Schatten norm. The space of pth Schatten-class operators is a Banach space with respect to the Schatten norm.
If we denote by the Banach space of compact operators on H with respect to the operator norm, the above Hölder-type inequality even holds for . From this it follows that , is a well-defined contraction. (Here the prime denotes (topological) dual.)