Abstract
Using radial sets of induced matrix norms, some maximal families S ⊆ M n such that ρ(AB) ρ(A)ρ(B) for all A , B ∈ S are identified. In the process new notions about matrix norms (such as adjustability of the spectral radius) are defined and used. As a result, certain further questions are raised. Mathematics subject classification (2000): 15A60, 65F35, 15A18.
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