Abstract
The spectral theorem exhibits normal operators as integrals with respect to some of their reducing subspaces. This is the most satisfying structure theorem known for operators on infinite-dimensional spaces: the class of normal operators is a large and useful class of operators and the spectral theorem is an appropriate tool for answering many questions about them. It should be noted, however, that the spectral theorem does not answer all questions about normal operators; in particular, there are still a number of unsolved problems about invariant subspaces of normal operators, (see Section 10.1).
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© 1973 Springer-Verlag Berlin Heidelberg
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Radjavi, H., Rosenthal, P. (1973). Normal Operators. In: Invariant Subspaces. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 77. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65574-6_2
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DOI: https://doi.org/10.1007/978-3-642-65574-6_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-65576-0
Online ISBN: 978-3-642-65574-6
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