Schatten Norm
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High Quality Content by WIKIPEDIA articles! In mathematics, specifically functional analysis, the Schatten norm arises as a generalization of p-integrability similar to the trace class norm and the Hilbert Schmidt norm. The norm is defined as T _{S_p} := bigg( sum _{xin sigma (T^ T)} x^{p/2}bigg)^{1/p} for pin [1,infty) and an operator T on the Hilbert space X. Here (T T) denotes the spectrum of the positive operator T T. This should be interpreted as a multiset. An operator which has a finite Schatten norm is called a Schatten class operator and the space of such operators is denoted by Sp(X)...
High Quality Content by WIKIPEDIA articles! In mathematics, specifically functional analysis, the Schatten norm arises as a generalization of p-integrability similar to the trace class norm and the Hilbert Schmidt norm. The norm is defined as T _{S_p} := bigg( sum _{xin sigma (T^ T)} x^{p/2}bigg)^{1/p} for pin [1,infty) and an operator T on the Hilbert space X. Here (T T) denotes the spectrum of the positive operator T T. This should be interpreted as a multiset. An operator which has a finite Schatten norm is called a Schatten class operator and the space of such operators is denoted by Sp(X). With this norm, Sp(X) is a Banach space, and a Hilbert space for p=2.
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