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Sublinearity and Other Spectral Conditions on a Semigroup
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- Journal:
- Canadian Journal of Mathematics / Volume 52 / Issue 1 / 01 February 2000
- Published online by Cambridge University Press:
- 20 November 2018, pp. 197-224
- Print publication:
- 01 February 2000
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- Article
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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.
