绝对平均有界数列空间A_(ab)(K)

Absolutely Average Bounded Number Sequence Space A_(ab)(K)

提出了绝对平均有界数列的概念,并由此定义了实(或复)数域K上绝对平均有界的数列空间Aab(K),这是一个介于有界数列空间l∞和近似有界数列空间Ab(K)之间的空间.给出了数列绝对平均有界性的等价条件,证明了空间Aab(K)是不可分的、不自反的、不具有Krern-Mil'man性质和Radon-Nikod m性质的Banach空间.

Based on the absolutely average convergence of a number sequence,the concept of absolutely average bounded number sequence is given.Space Aab（K） is defined as absolutely average bounded number sequences over the real or complex scalar field K,which is a space between space l∞ of bounded number sequences and space Ab（K） of approxmatively bounded number sequences.Moreover,that an equivalent condition of a number sequence is absolutely average bounded is given,and space Aab（K） is a non-separable,non-reflexive Banach space which has neither the Kren-Mil＇man property nor Radon-Nikodm property are proved.