مشخصات پژوهش

عنوان	Weight generalization of the space of continuous functionsvanishing at infinity
نوع پژوهش	مقاله چاپ‌شده در مجلات علمی
کلیدواژه‌ها	Banach space, locally compact space, topological algebra, weighted space
چکیده	In this paper, we characterize the weighted generalization of the space of continuous functions vanishing at infinity and correct some wrong results in the paper. Let 𝑋 be a locally compact space and 𝜈 is an arbitrary weight (non-negativefunction) on 𝑋. We give a correct and comprehensive definition of the weightedgeneralization 𝐶𝜈0 (𝑋) of 𝐶0(𝑋), and show that it is a seminormed space withrespect to the canonical seminorm ‖𝑓‖𝜈 = sup𝑥∈𝑋 |𝑓(𝑥)|, where 𝑓∈𝐶𝜈0 (𝑋). Wefind conditions on 𝜈 under which 𝐶𝜈0 (𝑋), with respect to ‖.‖𝜈, becomes a normedspace or a Banach space or an algebra, or a topological algebra, respectively.
پژوهشگران	رضا سالکی (نفر اول)، حجت اله سامع (نفر دوم)