Invariant linear functionals on L∞(R+)

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:481

Article

Kunisada, Ryoichi¹ 

[1] Waseda Univ, Fac Educ & Integrated Arts & Sci, Shinjuku Ku, Tokyo 1698050, Japan

关键词: Banach limits;    Invariant measures;    Summability methods;    Hardy operator;    Cesaro operator;   

DOI  :  10.1016/j.jmaa.2019.123452

来源: Elsevier

【 摘 要 】

We consider a continuous version of the classical notion of Banach limits, i.e., normalized positive linear functionals on L-infinity (R+) invariant under translations f (x) bar right arrow f(x + s) of L-infinity (R+) for every s >= 0. We give one of its characterizations in terms of the invariance under the operation of a certain linear transformation on L-infinity (R+). We also deal with invariant linear functionals under dilations f(x) bar right arrow f (rx), r >= 1 and give a similar characterization via the Hardy operator. Applications to summability methods are presented in the last section. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free