SOME WEIGHTED GROUP ALGEBRAS ARE OPERATOR ALGEBRAS

作者：Lee Hun Hee^*; Samei Ebrahim; Spronk Nico

来源：Proceedings of the Edinburgh Mathematical Society, 2015, 58(2): 499-519.

DOI：10.1017/S0013091514000212

• weighted group algebras
• operator algebras
• groups with polynomial growth
• Littlewood multipliers

Let G be a finitely generated group with polynomial growth, and let. be a weight, i.e. a submultiplicative function on G with positive values. We study when the weighted group algebra l(1)(G, omega) is isomorphic to an operator algebra. We show that l(1)(G, omega) is isomorphic to an operator algebra if. is a polynomial weight with large enough degree or an exponential weight of order 0 < alpha < 1. We demonstrate that the order of growth of G plays an important role in this problem. Moreover, the algebraic centre of l(1)(G, omega) is isomorphic to a Q-algebra, and hence satisfies a multi-variable von Neumann inequality. We also present a more detailed study of our results when G consists of the d-dimensional integers Z(d) or the three-dimensional discrete Heisenberg group H-3(Z). The case of the free group with two generators is considered as a counter-example of groups with exponential growth.

• 出版日期2015-6
• 单位Saskatoon; Saskatchewan