Norm Attaining Operators on Some Classical Banach Spaces

✍ Scribed by María D. Acosta; César Ruiz

• Publisher: John Wiley and Sons
• Year: 2002
• Tongue: English
• Weight: 184 KB
• Volume: 235
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/1522-2616(200202)235:1<17::aid-mana17>3.0.co;2-k

✦ Synopsis

We show that for the Köthe space X = c 0 + 1 (w), equipped with the Luxemburg norm, the set of norm attaining operators from X into any infinite-dimensional strictly convex Banach space Y is not dense in the space of all bounded operators. The same assertion holds for any infinitedimensional L 1 (µ). This gives the first example of a classical space X satisfying the previous property. We also prove that all the spaces c 0 + 1 (w) are isomorphic for a large class of weights w.