Self Adjoint Operators On Hilbert Space
Hilbert spaces are Banach spaces, so the above discussion applies to bounded operators on Hilbert spaces as well, although possible differences may arise from the adjoint operation on operators. For example, let H be a Hilbert space and T ∈ L(H), σ(T*) is not σ(T) but rather its image under complex conjugation.
For a self adjoint T ∈ L(H), the Borel functional calculus gives additional ways to break up the spectrum naturally.
Read more about this topic: Continuous Spectrum
Famous quotes containing the word space:
“A set of ideas, a point of view, a frame of reference is in space only an intersection, the state of affairs at some given moment in the consciousness of one man or many men, but in time it has evolving form, virtually organic extension. In time ideas can be thought of as sprouting, growing, maturing, bringing forth seed and dying like plants.”
—John Dos Passos (1896–1970)