Width Numbers and Interpolation

✍ Scribed by M. F. Teixeira

• Book ID: 102943011
• Publisher: John Wiley and Sons
• Year: 1984
• Tongue: English
• Weight: 658 KB
• Volume: 116
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19841160103

✦ Synopsis

These numbers, often referred to as WIDTH numbers, are important examples of the so-called s-numbers, whose theory for BANACR spaces is due to PIETSCH, cf. [S]. They are of proven importance in Functional Analysis and Applications, the main reason for this arising from the close relations between the sequence (sn(T)) of s-numbers of a bounded linear operator T and the distribution of its eigenvalues. As an illustration of this connection, we point out a remarkable result obtained by KONIG [a] for compact operators, which we shall use in this note. According to KONIG'S formula the eigenvalues I,(T) of T are given by liLn(l')I = lini ~, ( T m ) l / m , for all n E N .