Derived algebras in L₁ of a compact group

David S. Browder

Vol. 43 (1972), No. 1, 39–49

DOI: 10.2140/pjm.1972.43.39

Abstract

Let G be a compact topological group. In this paper, it is shown that the derived algebra D_p of L_p(G) (for 1 ≦ p < ∞) is contained in the ideal S_p of functions in L_p(G) with unconditionally convergent Fourier series. It is also noted that this inclusion can be strict if G is nonabelian. Finally, it is shown that the derived algebra of the center of L_p(G) is always equal to the center of S_p, generalizing a known result that D_p = |S_p when G is compact and abelian.

Mathematical Subject Classification 2000

Primary: 43A15

Milestones

Received: 24 July 1971

Revised: 6 June 1972

Published: 1 October 1972