The similarity orbit of a normal operator

Author:
L. A. Fialkow

Journal:
Trans. Amer. Math. Soc. **210** (1975), 129-137

MSC:
Primary 47A55; Secondary 47B15

DOI:
https://doi.org/10.1090/S0002-9947-1975-0374956-X

MathSciNet review:
0374956

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Abstract: If is a bounded normal operator on a separable Hilbert space , let denote the similarity orbit of in and let denote the set of all compact perturbations of elements of . It is proved that is norm closed in if and only if the spectrum (essential spectrum) of is finite. If the essential spectrum of is infinite and is a normal operator whose spectrum is connected and contains that of , then is in the closure of . If the spectrum of is connected, this result characterizes the normal elements of the closure of . A normal operator is similar to a nonquasidiagonal operator if and only if its essential spectrum contains more than two points.

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DOI:
https://doi.org/10.1090/S0002-9947-1975-0374956-X

Article copyright:
© Copyright 1975
American Mathematical Society