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Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators by Randall Eubank, Tailen Hsing

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4.5 Trace class operators

In the previous section, we introduced HS operators that provide an important subset of the compact operators. Another such subset is the trace class or nuclear operators that we examine in this section.

Let c04-math-599 be any bounded linear operator on some Hilbert space c04-math-600. By Theorem 3.4.3, we can define the square root of c04-math-601 as a bounded, nonnegative, self-adjoint operator c04-math-602 such that c04-math-603.

An argument ...

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