Remarks on n-normal operators
Keyword(s):
Let T be a bounded linear operator on a complex Hilbert space and n,m ? N. Then T is said to be n-normal if T+Tn = TnT+ and (n,m)-normal if T+mTn = TnT+m. In this paper, we study several properties of n-normal, (n,m)-normal operators. In particular, we prove that if T is 2-normal with ?(T) ? (-?(T)) ? {0}, then T is polarloid. Moreover, we study subscalarity of n-normal operators. Also, we prove that if T is (n,m)-normal, then T is decomposable and Weyl?s theorem holds for f (T), where f is an analytic function on ?(T) which is not constant on each of the components of its domain.
1969 ◽
Vol 21
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pp. 1421-1426
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2008 ◽
Vol 39
(4)
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pp. 347-352
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1969 ◽
Vol 12
(5)
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pp. 639-643
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2016 ◽
Vol 59
(2)
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pp. 354-362
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1974 ◽
Vol 76
(2)
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pp. 415-416
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Keyword(s):
1977 ◽
Vol 29
(5)
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pp. 1010-1030
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