Abstract
We study when a Banach space with absolute norm may have polynomial numerical indices equal to one. In the real case, we show that a Banach space X with absolute norm, which has the Radon-Nikodým property or is Asplund, satisfies n(2)(X)<1 unless it is one-dimensional. In the complex case, we show that the only Banach spaces X with absolute norm and the Radon-Nikodým property which satisfy n(2)(X)=1 are the spaces ℓ∞m. Also, the only Asplund complex space X with absolute norm which satisfies n(2)(X)=1 is c0(Λ).
Original language | English |
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Pages (from-to) | 400-408 |
Number of pages | 9 |
Journal | Linear Algebra and Its Applications |
Volume | 435 |
Issue number | 2 |
DOIs | |
State | Published - 15 Jul 2011 |
Keywords
- Absolute norm
- Köthe space
- Numerical index
- Polynomial