Unbounded operators and the Friedrichs extension
نویسنده
چکیده
In this note, by A ⊂ B, I mean that A is contained in B, and it may be that A = B; usually I write this by A ⊆ B, but A ⊂ B fits with the usual notation for saying that an operator is an extension of another. In this note, unless we say otherwise H denotes a Hilbert space over C, and we do not presume H to be separable. We shall write the inner product 〈·, ·〉 on H as conjugate linear in the second argument. We say that T is an operator in H if there is a linear subspace D(T ) of H such that T : D(T ) → H is a linear map. We call D(T ) the domain of T and R(T ) = T (D(T )) the range of T . We do not presume unless we say so that D(T ) is dense in H, and we say that T is densely defined when this is so. Define G (T ) = {(x, Tx) : x ∈ D(T )},
منابع مشابه
Math 713 Spring 2010 Lecture Notes on Functional Analysis
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