A Note on Spectral Sublinearity for Collections of Positive Compact Operators on Banach Lattices
In this paper we consider the question when a triangularizable semigroup S of positive compact ideal-triangularizable operators on an order continuous Banach lattice X is ideal-triangularizable. We prove that triangularizability always implies ideal-triangularizability iff X contains at most one ato...
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-09-01
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| Series: | Special Matrices |
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| Online Access: | https://doi.org/10.1515/spma-2018-0029 |
| Summary: | In this paper we consider the question when a triangularizable semigroup S of positive compact ideal-triangularizable operators on an order continuous Banach lattice X is ideal-triangularizable. We prove that triangularizability always implies ideal-triangularizability iff X contains at most one atom. Under this condition we connect ideal-triangularizability of S with spectral properties of S. Surprisingly, S is idealtriangularizable iff the spectral radius is subadditive on S iff the spectral radius is submultiplicative on S. We also consider a pair of positive compact operators A and T with the property that A has a T-stable spectrum. |
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| ISSN: | 2300-7451 |