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- W1978510897 abstract "A quadratic operator Q of Hilbert-Schmidt class on a real separable Hilbert space H is shown to be uniquely representable as a sequence of self-adjoint linear operators of Hilbert-Schmidt class on H , such that Q(x) = Σ k 〈L k x, x〉u k with respect to a Hilbert basis . It is shown that with the norm | ‖ Q ‖ | = (Σ k ‖ L k ‖ 2 ) ½ and inner-product 〈〈〈 Q, P 〉〉〉 = Σ k 〈〈 L k , M k 〉〉, together with a multiplication defined componentwise through the composition of the linear components, the vector space of all Hilbert-Schmidt quadratic operators Q on H becomes a linear H *-algebra containing an ideal of nuclear (trace class) quadratic operators. In the finite dimensional case, each Q is also shown to have another representation as a block-diagonal matrix of Hilbert-Schmidt class which simplifies the practical computation and manipulation of quadratic operators." @default.
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- W1978510897 date "1990-02-01" @default.
- W1978510897 modified "2023-09-27" @default.
- W1978510897 title "A Hilbert algebra of Hilbert-Schmidt quadratic operators" @default.
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- W1978510897 doi "https://doi.org/10.1017/s0004972700017913" @default.
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