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Volterra Semigroups Have Invariant Subspaces

✍ Scribed by Yu.V. Turovskii


Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
111 KB
Volume
162
Category
Article
ISSN
0022-1236

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✦ Synopsis


It is proved that any multiplicative semigroup consisting of compact quasinilpotent operators on a Banach space is triangularizable. The consequences are discussed.


πŸ“œ SIMILAR VOLUMES


Invariant Subspaces for Semigroups of Al
✍ Grega Cigler; Roman DrnovΕ‘ek; Damjana Kokol-BukovΕ‘ek; MatjaΕΎ Omladič; Thomas J. πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 239 KB

269 305) that a semigroup of matrices is triangularizable if the ranks of all the commutators of elements of the semigroup are at most 1. Our main theorem is an extension of this result to semigroups of algebraic operators on a Banach space. We also obtain a related theorem for a pair [A, B] of arbi