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Riesz operators and Schur’s lemma

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Abstract

We present sufficient conditions in order (the space of) a Riesz operator T in a Hilbert space H have a Jordan-Schur basis with respect to a scalar product equivalent to the original one. This is related to Schur’s lemma for a compact operator, which is an extension of Schur’s classical theorem on unitary triangularization in a finite dimensional space. The finite dimensional case is also studied.

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Authors and Affiliations

  1. Department of Analysis, Institute of Mathematics, University of Technology and Economics, Budapest, H-1521, Hungary

    Béla Nagy

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  1. Béla Nagy
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Correspondence to Béla Nagy.

Additional information

Communicated by L. Kérchy

This research was supported by the Hungarian OTKA Grant No. K77748.

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Nagy, B. Riesz operators and Schur’s lemma. ActaSci.Math. 80, 639–650 (2014). https://doi.org/10.14232/actasm-012-092-8

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  • DOI: https://doi.org/10.14232/actasm-012-092-8

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