Some results about diagonal operators on Köthe echelon spaces
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Several questions about diagonal operators between Köthe echelon spaces are investigated: (1) The spectrum is characterized in terms of the Köthe matrices defining the spaces, (2) It is characterized when these operators are power bounded, mean ergodic or uniformly mean ergodic, and (3) A description of the topology in the space of diagonal operators induced by the strong topology on the space of all operators is given.
KeywordsEchelon spaces Diagonal operators Mean ergodic operators Power bounded operators
Mathematics Subject Classification47B37 47A10 46A45
The author would like to express his gratitude to his advisors José Bonet and Enrique Jordá for their guidance and their valuable suggestions and comments.
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