Quantitative and qualitative estimates on the norm of products of polynomials

Abstract

When for the first time, in 1987, a Banach space X and a bounded operator T: XX without nontrivial invariant subspaces was constructed, one of the many tools used was a series of estimates on the norm of a product of polynomials. Here, we continue this study of estimates on the norm of a product of polynomials by, on the one hand, extending some results due to Beauzamy and Enflo and, on the other, observing that an inequality by Borwein and Erdelyi holds in a more general context.

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Acknowledgements

The authors would like to thank the referee, whose insightful remarks improved the presentation of this work. G. A. Muñoz-Fernández and J. B. Seoane-Sepúlveda were supported by Grant 1PGC2018-097286-B-I00.

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Correspondence to Juan B. Seoane-Sepúlveda.

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Araújo, G., Enflo, P.H., Muñoz-Fernández, G.A. et al. Quantitative and qualitative estimates on the norm of products of polynomials. Isr. J. Math. 236, 727–745 (2020). https://doi.org/10.1007/s11856-020-1987-y

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