On totally paranormal operators
2002 ◽
Vol 66
(3)
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pp. 425-441
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Keyword(s):
A continuous linear operator on a complex Banach space is said to be paranormal if ‖Tx‖2 ≤ ‖T2x‖ ‖x‖ for all x ∈ X. T is called totally paranormal if T–λ is paranormal for every λ ∈ C. In this paper we investigate the class of totally paranormal operators. We shall see that Weyl's theorem holds for operators in this class. We also show that for totally paranormal operators the Weyl spectrum satisfies the spectral mapping theorem. In Section 5 of this paper we investigate the operator equations eT = eS and eTeS = eSeT for totally paranormal operators T and S.
1968 ◽
Vol 8
(1)
◽
pp. 119-127
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1983 ◽
Vol 26
(2)
◽
pp. 163-167
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Keyword(s):
2001 ◽
Vol 14
(3)
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pp. 303-308
◽
1998 ◽
Vol 220
(2)
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pp. 760-768
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2004 ◽
Vol 76
(2)
◽
pp. 291-302
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2008 ◽
Vol 77
(3)
◽
pp. 515-520
1974 ◽
Vol 26
(6)
◽
pp. 1384-1389
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1977 ◽
Vol 20
(4)
◽
pp. 293-299
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