This is an announcement for the paper “Primarity of direct sums of Orlicz spaces and Marcinkiewicz spaces” by Jose L. Ansorenahttps://arxiv.org/search/math?searchtype=author&query=Ansorena%2C+J+L.
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:1804.01372https://arxiv.org/abs/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.