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- W4302436260 abstract "What is an adequate extension of an operator ideal I to the polynomial and multilinear settings? This question motivated the appearance of the concepts of coherent sequences of polynomial ideals and compatibility of a polynomial ideal with an operator ideal, introduced by D. Carando el al. We propose a different approach by considering pairs (U_{k},M_{k})_{k=1}^{infty}, where (U_{k})_{k=1}^{infty} is a polynomial ideal and (M_{k})_{k=1}^{infty} is a multi-ideal, instead of considering just polynomial ideals. Our approach ends a discomfort caused by the previous theory: for real scalars the canonical sequence (P_{k})_{k=1}^{infty} of continuous k-homogeneous polynomials is not coherent according to the definition of Carando et al." @default.
- W4302436260 created "2022-10-06" @default.
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- W4302436260 date "2011-01-10" @default.
- W4302436260 modified "2023-09-27" @default.
- W4302436260 title "On multi-ideals and polynomial ideals of Banach spaces: a new approach to coherence and compatibility" @default.
- W4302436260 doi "https://doi.org/10.48550/arxiv.1101.1992" @default.
- W4302436260 hasPublicationYear "2011" @default.
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