Generalized Entropy Numbers and Gelfand Numbers – an Approach to the Entropy Behaviour of Certain Integral Operators

✍ Scribed by Bernd Carl; Irmtraud Stephani

• Publisher: John Wiley and Sons
• Year: 1987
• Tongue: English
• Weight: 865 KB
• Volume: 132
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19871320110

✦ Synopsis

An essential point of view was of course the question how generalized entropy numbers and entropy ideals can be employed for getting informations about the usual entropy numbers e,(T) and thus about the degree of compactness of an operator T in the usual sense. It turned out that reiteration and factorization properties of generalized entropy ideals are a key to this problem. I n [4] among others the authors determined the entropy behaviour of certain r-nuclear operators in the sense of GROTHENDIECK by these methods.

9'

* sup kPa,(S; A ) with q=-, which is a consequence of (1.3), and of which results from (1.8), we reach (1.7) without difficulties. U,(S ; A ) s 3 x a k ( T ; A ) 9