Ergodicity and stability of orbits of unbounded semigroup representations

Journal of the Australian Mathematical Society

Bolis Basit¹ 

[1] A. J. Pryde

关键词: primary 46J20;    43A60;    secondary 47A35;    34K25;    28B05;   

DOI  :  10.1017/S1446788700013598

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

We develop a theory of ergodicity for unbounded functions ø: J → X, where J is a subsemigroup of a locally compact abelian group G and X is a Banach space. It is assumed that ø is continuous and dominated by a weight w defined on G. In particular, we establish total ergodicity for the orbits of an (unbounded) strongly continuous representation T: G → L(X) whose dual representation has no unitary point spectrum. Under additional conditions stability of the orbits follows. To study spectra of functions, we use Beurling algebras L1w(G) and obtain new characterizations of their maximal primary ideals, when w is non-quasianalytic, and of their minimal primary ideals, when w has polynomial growth. It follows that, relative to certain translation invariant function classes , the reduced Beurling spectrum of ø is empty if and only if ø ∈ . For the zero class, this is Wiener's tauberian theorem.

【 授权许可】

Unknown