Abstract Cesaro spaces. Duality

作者：Lesnik Karol^*; Maligranda Lech

来源：Journal of Mathematical Analysis and Applications, 2015, 424(2): 932-951.

DOI：10.1016/j.jmaa.2014.11.023

• Cesaro function spaces
• Cesaro operator
• Banach ideal spaces
• Symmetric spaces
• Dual spaces
• Kothe dual spaces

We study abstract Cesaro spaces CX, which may be regarded as generalizations of Cesaro sequence spaces ces(p) and Cesaro function spaces Ces(p)(I) on I = [0,1] or I = [0, infinity), and also as the description of optimal domain from which Cesaro operator acts to X. We find the dual of such spaces in a very general situation. What is however even more important, we do it in the simplest possible way. Our proofs are more elementary than the known ones for ces(p) and Ces(p)(I). This is the point how our paper should be seen, i.e. not as a generalization of known results, but rather like grasping and exhibiting the general nature of the problem, which is not so easily visible in previous publications. Our results show also an interesting phenomenon that there is a big difference between duality in the cases of finite and infinite intervals.

• 出版日期2015-4-15