Amenability Properties of Rajchman Algebras

作者：Ghandehari Mahya^*

来源：Indiana University Mathematics Journal, 2012, 61(3): 1369-1392.

DOI：10.1512/iumj.2012.61.4622

• Rajchman algebra
• Fourier algebra
• Fourier-Stieltjes algebra
• locally compact groups
• amenability
• operator amenability
• bounded approximate identity

Rajchman measures of locally compact abelian groups have been studied for almost a century now, and they play an important role in the study of trigonometric series. Eymard%26apos;s influential work allowed generalizing these measures to the case of non-abelian locally compact groups G. The Rajchman algebra of G, which we denote by B-0(G), is the set of all elements of the Fourier-Stieltjes algebra that vanish at infinity. %26lt;br%26gt;In the present article, we characterize the locally compact groups that have amenable Rajchman algebras. We show that B-0(G) is amenable if and only if G is compact and almost abelian. On the other extreme, we present many examples of locally compact groups, such as non-compact abelian groups and infinite solvable groups, for which B-0(G) fails to even have an approximate identity.

• 出版日期2012