The Spectral Theorem is a milestone in the theory of Hilbert space operators, providing a full statement about the nature and structure of normal operators. For compact normal operators the Spectral Theorem can be completely investigated without requiring any knowledge of measure theory, and this leads to the concept of diagonalization. However, the Spectral Theorem for plain normal operators (the general case) requires some (elementary) measure theory.
KeywordsHilbert Space Normal Operator Spectral Measure Compact Operator Positive Measure
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