MAD Families of Projections on l^2 and Real-Valued Functions on Omega

Abstract

Two sets are said to be almost disjoint if their intersection is finite. Almost disjoint subsets of [omega]^omega and omega^omega have been studied for quite some time. In particular, the cardinal invariants a and a_e, defined to be the minimum cardinality of a maximal infinite almost disjoint family of [omega]^omega and omega^omega respectively, are known to be consistently less than continuum. Here we examine analogs for functions in R^omega and projections on l^2, showing that they too can be consistently less than continuum.