A note on Jordan-von Neumann constant and James constant

作者：Yang Changsen^*

来源：Journal of Mathematical Analysis and Applications, 2009, 357(1): 98-102.

DOI：10.1016/j.jmaa.2009.04.002

• von Neumann-Jordan constant
• James constant

Let X be a non-trivial Banach space. L. Maligranda conjectured C(NJ)(X) <= 1 J(X)(2)/4 for James constant J(X) and von Neumann-Jordan constant C(NJ)(X) of X. Satit Saejung gave a proof of it in 2006. In this note, we show that the last step in Satit Saejung's proof is not valid. Using his proof, the result should be C(NJ)(X) <= 1 J(X)(2)/4 J(X)root 4 (2-J(X))(2)-2/4. On the other hand, we give a new proof of C(NJ)(X) <= 1 J(X)(2)/4. As an application, we give a relation between J(X) and J(I(p)(X)).

• 出版日期2009-9-1
• 单位河南师范大学