Absolute Norms on Cn

✍ Scribed by Kichi-Suke Saito; Mikio Kato; Yasuji Takahashi

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 167 KB
• Volume: 252
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.2000.7139

✦ Synopsis

In this paper, we study the absolute normalized norms on ‫ރ‬ n . We show that the set of all absolute normalized norms on ‫ރ‬ n is in one-to-one correspondence with the set ⌿ of all continuous convex functions on ⌬ with some suitable conditions,

As some applications, we show that an absolute norm on ‫ރ‬ is strictly convex if and only if the corresponding function on ⌬ is strictly convex. Further, we n consider the von Neumann᎐Jordan constant of ‫ރ‬ n with an absolute normalized norm.