Li Zhong
The problem of eigenvalues and eigenvectors of a linear operator is an important and better-understood one. To find eigenvalues and (possibly generalized) eigenvectors, it is equivalent to decompose the space into a direct sum/integral of eigenspaces. We will start from finite dimensional spaces, and then go to the case of compact operators on a Hilbert space. After these discussion, the general problem for a bounded normal operator is stated and answered in the classical language. We then proceed to introduce the concept of Hilbert bundles and try to use it to reformulate and trivialize the original problem.
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