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On normal extensions of unbounded operators. III: Spectral properties. (English) Zbl 0721.47009
This is the last part of the authors’ triology devoted to systematic exposition of the fundamentals of the theory of unbounded subnormal operators [for part II see Acta Sci. Math. 53, No.12, 153-177 (1989; Zbl 0698.47003)]. The present part concerns spectral properties of subnormal oprators as related to those of their normal extensions. Though minimality of spectral type need not entail uniqueness (they give such an example), it is shown that the basic spectral inclusion property holds true. Suppose that an unbounded subnormal operator S leaves its domain invariant and it has at least one minimal normal extension of cyclic type. Then the authors show that an arbitrary normal extension of S is minimal of spectral type if and only if it is minimal of cyclic type. Moreover they give sufficient conditions for that S has a minimal normal extension of cyclic type. The paper contains researches of analytic models of cyclic unbounded subnormal operators.

MSC:
47A20Dilations, extensions and compressions of linear operators
47B25Symmetric and selfadjoint operators (unbounded)
47B20Subnormal operators, hyponormal operators, etc.
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References:
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