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1. CJM 2000 (vol 52 pp. 197)

 Sublinearity and Other Spectral Conditions on a Semigroup Subadditivity, sublinearity, submultiplicativity, and other conditions are considered for spectra of pairs of operators on a Hilbert space. Sublinearity, for example, is a weakening of the well-known property~$L$ and means $\sigma(A+\lambda B) \subseteq \sigma(A) + \lambda \sigma(B)$ for all scalars $\lambda$. The effect of these conditions is examined on commutativity, reducibility, and triangularizability of multiplicative semigroups of operators. A sample result is that sublinearity of spectra implies simultaneous triangularizability for a semigroup of compact operators. Categories:47A15, 47D03, 15A30, 20A20, 47A10, 47B10