Abstract
It is known that Cesàro means of polynomial powers of contractive operators in Hilbert spaces converge strongly. We address the question of whether the limit is a projection. We show that the only polynomials leading to projections for any operator are of degree at most one. Moreover, we find a spectral characterisation of operators in Hilbert spaces that have a projection as the limit of their polynomial Cesàro means for every reasonable polynomial.
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Kunszenti-Kovács, D., Nittka, R. & Sauter, M. On the limits of Cesàro means of polynomial powers. Math. Z. 268, 771–776 (2011). https://doi.org/10.1007/s00209-010-0694-5
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DOI: https://doi.org/10.1007/s00209-010-0694-5
Keywords
- Polynomial Cesàro averages
- Unconventional ergodic means
- Projections
- Roots of unity
- Permutation polynomials