ALGEBRAIC EQUIVALENCE OF QUASINORMAL OPERATORS
Keyword(s):
Let $T_j =N_j\oplus( S\otimes A_j)$ be quasinormal, where $N_j$ is normal and $A_j$ is a positive definite operator, $j = 1, 2$. We show that $T_1$ is algebraically equivalent to $T_2$ if and only if $\sigma(A_1) =\sigma(A_2)$ and $\sigma(N_1)\backslash\sigma_{ap}(S\otimes A_1) =\sigma(N_2)\backslash\sigma_{ap}(S\otimes A_2)$. This generalizes the corresponding result for normal and isometric operators.
1989 ◽
Vol 41
(6)
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pp. 677-681
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Keyword(s):
1978 ◽
Vol 9
(5)
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pp. 855-866
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Keyword(s):
1981 ◽
Vol 40
(1)
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pp. 54-65
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2010 ◽
Vol 2010
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pp. 1-7
2001 ◽
Vol 27
(3)
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pp. 155-160
1998 ◽
Vol 109
(2)
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pp. 385-391
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2020 ◽
Vol 23
(6)
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pp. 1605-1646
2003 ◽
Vol 40
(4)
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pp. 603-611
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