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On Permutability and Submultiplicativity of Spectral Radius

  • W. E. Longstaff (a1) and H. Radjavi (a2)

Abstract

Let 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.

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Copyright

References

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On Permutability and Submultiplicativity of Spectral Radius

  • W. E. Longstaff (a1) and H. Radjavi (a2)

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