Primarity of direct sums of Orlicz spaces and Marcinkiewicz spaces

Jose L. Ansorena

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arXiv · 1809.05749

Primarity of direct sums of Orlicz spaces and Marcinkiewicz spaces

Jose L. Ansorena

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Abstract

Let $\mathbb{Y}$ be either an Orlicz sequence space or a Marcinkiewicz sequence space. We take advantage of the recent advances in the theory of factorization of the identity carried on in [R. Lechner, Subsymmetric weak* Schauder bases and factorization of the identity, arXiv:1804.01372 [math.FA]] to provide conditions on $\mathbb{Y}$ that ensure that, for any $1\le p\le\infty$, the infinite direct sum of $\mathbb{Y}$ in the sense of $\ell_p$ is a primary Banach space, enlarging this way the list of Banach spaces that are known to be primary.

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Jose L. Ansorena. 2018-09-15. Primarity of direct sums of Orlicz spaces and Marcinkiewicz spaces. https://arxiv.org/abs/1809.05749

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