Geodesic
On nth roots of normal operators
Filomat, Tome 34 (2020) no. 8, p. 2797

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DOI

For n-normal operators A [2, 4, 5], equivalently n-th roots A of normal Hilbert space operators, both A and A * satisfy the Bishop–Eschmeier–Putinar property (β) , A is decomposable and the quasi-nilpotent part H 0 (A − λ) of A satisfies H 0 (A − λ) −1 (0) = (A − λ) −1 (0) for every non-zero complex λ. A satisfies every Weyl and Browder type theorem, and a sufficient condition for A to be normal is that either A is dominant or A is a class A(1, 1) operator.
DOI : 10.2298/FIL2008797D
Classification : 47A05, 47A55, 47A80, 47A10
Keywords: Normal operator, n-th root, property (β), decomposable, quasi-nilpotent part, pole, dominant operator, Weyl and Browder theorems 
B P Duggal; I H Kim. On nth roots of normal operators. Filomat, Tome 34 (2020) no. 8, p. 2797 . doi: 10.2298/FIL2008797D
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     title = {On nth roots of normal operators},
     journal = {Filomat},
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     year = {2020},
     volume = {34},
     number = {8},
     doi = {10.2298/FIL2008797D},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2008797D/}
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