Geodesic
On Permutability and Submultiplicativity of Spectral Radius
Canadian journal of mathematics, Tome 47 (1995) no. 5, pp. 1007-1022

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-1995-053-x
Mots-clés : 47A15, 47D03, 47A10, 20M20, 15A30 
Longstaff, W. E.; Radjavi, H. On Permutability and Submultiplicativity of Spectral Radius. Canadian journal of mathematics, Tome 47 (1995) no. 5, pp. 1007-1022. doi: 10.4153/CJM-1995-053-x
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