中文摘要：

周知任意λ〉0,内积空间具有Pλ性质,并且其非方常数为√2,空间具有P1性质,推不出空间是内积空间,但是容易推出空间的非方常数也为√2.构造了一个具有旋转不变性质的赋范空间,该空间具有P√3性质,计算得到其非方常数为2√3-2,间接地说明了对于某特定的λ〉0,具有Pλ性质的赋范空间其非方常数不一定为√2,同时也说明了具有Pλ性质并不能保证空间的严格凸性或一致凸性。

英文摘要：

It is well known that inner product spaces satisfy property Pλ for arbitrary λ 〉 0, and the nonsquare constants of them are √2. The spaces satisfying property P1 are not certainly inner product spaces, but we easily know that the nonsquare constants of these spaces are also √2. A normed linear space with invariability under rotation and property P√3 is constructed, and it is easy to see that the nonsquare constant of the space is 2√3 - 2, which show that the nonsquare constant of the normed linear space satisfying property Pλ is not certainly √2 for some special A, and normed linear spaces satisfying property Pλ are not necessarily rotund or uniformly rotund.