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The Cesàro operator on smooth sequence spaces of finite type

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

The discrete Cesàro operator \(\mathsf {C}\) is investigated in the class of smooth sequence spaces \(\lambda _0(A)\) of finite type. This class contains properly the power series spaces of finite type. Of main interest is its spectrum, which is distinctly different in the cases when \(\lambda _0(A)\) is nuclear and when it is not. The nuclearity of \(\lambda _0(A)\) is characterized via certain properties of the spectrum of \(\mathsf {C}\). Moreover, \(\mathsf {C}\) is always power bounded and uniformly mean ergodic on \(\lambda _0(A)\).

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Acknowledgements

The author wishes to thank Prof. José Bonet for crucial suggestions and discussions. He is also thankful to the anonymous referees as well as Prof. David Jornet for their careful reviewing.

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  1. Instituto Universitario de Matemática Pura y Aplicada (IUMPA), Universitat Politècnica de València, 46071, Valencia, Spain

    Ersin Kızgut

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  1. Ersin Kızgut
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Kızgut, E. The Cesàro operator on smooth sequence spaces of finite type. RACSAM 113, 1747–1763 (2019). https://doi.org/10.1007/s13398-018-0578-9

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