Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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) an ...Täielik kirjeldus
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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.