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We show that the non-separable Banach space $SL^infty$ is primary. This is achieved by directly solving the infinite dimensional factorization problem in $SL^infty$. In particular, we bypass Bourgains localization method.
In this paper we consider the following problem: Let $X_k$, be a Banach space with a normalized basis $(e_{(k,j)})_j$, whose biorthogonals are denoted by $(e_{(k,j)}^*)_j$, for $kinmathbb{N}$, let $Z=ell^infty(X_k:kinmathbb{N})$ be their $ell^infty$-
We classify the simple bounded weight modules of ${mathfrak{sl}(infty})$, ${mathfrak{o}(infty)}$ and ${mathfrak{sp}(infty)}$, and compute their annihilators in $U({mathfrak{sl}(infty}))$, $U({mathfrak{o}(infty))}$, $U({mathfrak{sp}(infty))}$, respectively.
We prove that the negative infinitesimal generator $L$ of a semigroup of positive contractions on $L^infty$ has a bounded $H^infty(S_eta^0)$-calculus on the associated Poisson semigroup-BMO space for any angle $eta>pi/2$, provided the semigroup satis
Let $1leq p,q < infty$ and $1leq r leq infty$. We show that the direct sum of mixed norm Hardy spaces $big(sum_n H^p_n(H^q_n)big)_r$ and the sum of their dual spaces $big(sum_n H^p_n(H^q_n)^*big)_r$ are both primary. We do so by using Bourgains local
$SL^infty$ denotes the space of functions whose square function is in $L^infty$, and the subspaces $SL^infty_n$, $ninmathbb{N}$, are the finite dimensional building blocks of $SL^infty$. We show that the identity operator $I_{SL^infty_n}$ on $SL^in