Primarity of direct sums of Orlicz spaces and Marcinkiewicz spaces

Abstract

Let 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 by Lechner [12] to provide conditions on Y that ensure that, for any 1 ≤ p ≤ ∞, the infinite direct sum of Y in the sense of ℓ p is a primary Banach space, enlarging this way the list of Banach spaces that are known to be primary.2010 Mathematics Subject Classification. 46B25, 46B26, 46B15, 46B45.