On Permutability and Submultiplicativity of Spectral Radius
1995 ◽
Vol 47
(5)
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pp. 1007-1022
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Keyword(s):
AbstractLet r(T) denote the spectral radius of the operator T acting on a complex Hilbert space H. Let S be a multiplicative semigroup of operators on H. We say that r is permutable on 𝓢 if r(ABC) = r(BAC), for every A,B,C ∈ 𝓢. We say that r is submultiplicative on 𝓢 if r(AB) ≤ r(A)r(B), for every A, B ∈ 𝓢. It is known that, if r is permutable on 𝓢, then it is submultiplicative. We show that the converse holds in each of the following cases: (i) 𝓢 consists of compact operators (ii) 𝓢 consists of normal operators (iii) 𝓢 is generated by orthogonal projections.
2017 ◽
Vol 11
(01)
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pp. 1850004
Keyword(s):
1969 ◽
Vol 21
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pp. 1421-1426
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1974 ◽
Vol 26
(1)
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pp. 115-120
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Keyword(s):
1988 ◽
Vol 103
(3)
◽
pp. 473-480
Keyword(s):
1980 ◽
Vol 21
(1)
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pp. 75-79
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1981 ◽
Vol 23
(3)
◽
pp. 471-475
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