Some results about diagonal operators on Köthe echelon spaces

Abstract

2959 2968 113 4 ; S Krengel, U.: Ergodic Theorems. de Gruyter, Berlin (1985) ; [EN] 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. This research was partially supported by MINECO Project MTM2016-76647-P and the grant PAID-01-16 of the Universitat Politècnica de València. Agathen, S., Bierstedt, K.D., Bonet, J.: Projective limits of weighted (LB)-spaces of continuous functions. Arch. Math. 92, 384–398 (2009) Albanese, A.A., Bonet, J., Ricker, W.J.: Mean ergodic operators in Fréchet spaces. Ann. Acad. Sci. Fenn. Math. 34(2), 401–436 (2009) Bennett, G.: Some elementary inequalities. Quart. J. Math. 38, 401–425 (1987) Bennett, G.: Factorizing the classical inequalities. Mem. Am. Math. Soc. (1996). https://doi.org/10.1090/memo/0576 Bierstedt, K.D.: An introduction to locally convex inductive limits, Functional analysis and its applications (Nice, 1986), 35–133, ICPAM Lecture Notes. World Sci. Publishing, Singapore (1988) Bierstedt, K.D., Bonet, J.: Some aspects of the modern theory of Fréchet spaces. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 97(2), 159–188 (2003) Bierstedt, K.D., Meise, R., Summers, W.H.: Köthe sets and Köthe sequence spaces, Functional Analysis, Holomorphy and Approximation Theory. North-Holland Math. Studies 71, 27–91 (1982) Bonet, J., Jordá, E., Rodríguez-Arenas, A.: Mean ergodic multiplication operators on weighted spaces of continuous functions. Mediterr. J. Math 15, 108 (2018) Crofts, G.: Concerning perfect Fréchet spaces and transformations. Math. Ann. 182, 67–76 (1969) Kellogg, C.N.: An extension of the Hausdorff–Young theorem. Michig. Math. J. 18, 121–127 (1971) Meise, R., Vogt, D.: Introduction to Functional ...