摘要
赋范线性空间称为满足球覆盖性质,若其单位球面可被可数个不包含原点的闭球覆盖.考虑了C_(b)(R)和L^(∞)(R)两个例子上的等价范数|·|_(a)和‖·‖_(λ),得到两个结果:(C_(b)(R),|·|_(a))满足足球覆盖性质当且仅当a∈(1/2,1];(L^(∞)(R),‖·‖_(λ))在λ∈[0,1]时均不满足足球覆盖性质.
A normed vector space has the ball-covering property if its unit sphere can be covered by countably many closed balls off the origin.Two new examples,C_(b)(R)and L^(∞)(R),are considered by introducing new but equivalent norms(|·|_(a)和‖·‖_(λ))of them.(C_(b)(R),|·|_(a))has the ball-covering property if and only if a a∈(1/2,1].And for allλ∈[0,1],(L^(∞)(R),‖·‖_(λ))fails the ball-covering property.
作者
张睿杰
王彦桥
朱书辰
刘锐
Zhang Ruijie;Wang Yanqiao;Zhu Shuchen;Liu Rui(School of Mathematical Sciences and LPMC,Nankai University,Tianjin 300071,China)
出处
《南开大学学报（自然科学版）》
CAS
CSCD
北大核心
2023年第5期59-63,共5页
Acta Scientiarum Naturalium Universitatis Nankaiensis
基金
Partially supported by NNSFC(11671214,11971348,12071230)
National College Students Innovation and Entrepreneurship Training Program(202210055048)
Hundred Young Academia Leaders Program of Nankai University(63223027,91923104,91823003,63174012,ZB22000105)
Functional Analysis Teaching Funds of Nankai University(NKJG2022053)。
关键词
球覆盖
有界函数空间
本性有界函数空间
ball-covering property
bounded function space
equivalent norm
