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- W4287553660 abstract "We provide a new extension of Pitt's theorem for compact operators between quasi-Banach lattices, which permits to describe unconditional bases of finite direct sums of Banach spaces $mathbb{X}_{1}oplusdotsoplusmathbb{X}_{n}$ as direct sums of unconditional bases of its summands. The general splitting principle we obtain yields, in particular, that if each $mathbb{X}_{i}$ has a unique unconditional basis (up to equivalence and permutation), then $mathbb{X}_{1}oplus cdotsoplusmathbb{X}_{n}$ has a unique unconditional basis too. Among the novel applications of our techniques to the structure of Banach and quasi-Banach spaces we have that the space $ell_2oplus mathcal{T}^{(2)}$ has a unique unconditional basis." @default.
- W4287553660 created "2022-07-25" @default.
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- W4287553660 creator A5075301768 @default.
- W4287553660 date "2020-12-12" @default.
- W4287553660 modified "2023-09-29" @default.
- W4287553660 title "Uniqueness of unconditional basis of $ell_{2}oplus mathcal{T}^{(2)}$" @default.
- W4287553660 doi "https://doi.org/10.48550/arxiv.2012.06783" @default.
- W4287553660 hasPublicationYear "2020" @default.
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