✦ LIBER ✦

An inequality between Jordan–von Neumann constant and James constant

✍ Scribed by Changsen Yang; Haiying Li

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 356 KB
Volume: 23
Category: Article
ISSN: 0893-9659
DOI: 10.1016/j.aml.2009.09.023

No coin nor oath required. For personal study only.

✦ Synopsis

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) for X . Recently, J. Alonso et al. gave a proof of it and conjectured that C NJ (X) ≤ J(X ) is also valid. In this paper, we show that this conjecture is true.

📜 SIMILAR VOLUMES

On James and Jordan–von Neumann Constant

On James and Jordan–von Neumann Constants of Lorentz Sequence Spaces

✍ Mikio Kato; Lech Maligranda 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 88 KB

The nonsquare or James constant J X and the Jordan-von Neumann constant C NJ X are computed for two-dimensional Lorentz sequence spaces d 2 w q in the case where 2 ≤ q < ∞. The Jordan-von Neumann constant is also calculated in the case where 1 ≤ q < 2.