Vol. 43, No. 1, 1972

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Derived algebras in L1 of a compact group

David S. Browder

Vol. 43 (1972), No. 1, 39–49
Abstract

Let G be a compact topological group. In this paper, it is shown that the derived algebra Dp of Lp(G) (for 1 p < ) is contained in the ideal Sp of functions in Lp(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 Lp(G) is always equal to the center of Sp, generalizing a known result that Dp = |Sp 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
Authors
David S. Browder