Uniqueness of $E_\infty$ structures for connective covers

Abstract

We refine our earlier work on the existence and uniqueness of E∞ structures on K- theoretic spectra to show that at each prime p, the connective Adams summand l has a unique structure as a commutative S-algebra. For the p-completion lp we show that the McClure- Staffeldt model for lp is equivalent as an E∞ ring spectrum to the connective cover of the periodic Adams summand Lp. We establish a Bousfield equivalence between the connective cover of the Lubin-Tate spectrum En and BPh ni .