Abstract
The notion of the spectral multiplicity plays an important role in the theory of self-adjoint and normal operators. It serves a complete unitary invariant for operators of these classes, and in fact forms a background of the whole theory. As the main object it is proved to be the multiplicity function µ N (·) of a normal operator N on a separable Hubert space H, i.e. the dimension function
of the spectral decomposition of N
,
where ≅ stands for a unitary equivalence and λ for a Borel (scalar) spectral measure of N .In principle, all properties of N can be derived from properties of the multiplicity function µ N (·). In the case of a pure point spectrum one has simply
.
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Nikolskii, N.K. (1989). Multicyclicity Phenomenon. I. An Introduction and Maxi-Formulas. In: Nikolskii, N.K. (eds) Toeplitz Operators and Spectral Function Theory. Operator Theory: Advances and Applications, vol 42. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5587-7_1
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