Abstract
The only infinite-dimensional complex space with 1-unconditional basis which has polynomial numerical index of order 2 equal to 1 is c 0. In the real case, there is no space of this type. We also show that, in the complex case, if X is an infinite-dimensional Banach sequence space with absolute norm whose Köthe dual is norming and has polynomial numerical index of order 2 equal to 1, then c 0⊂X⊂ℓ ∞. In the real case, again there is no space of this type.
Original language | English |
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Pages (from-to) | 2001-2008 |
Number of pages | 8 |
Journal | Linear Algebra and Its Applications |
Volume | 437 |
Issue number | 8 |
DOIs | |
State | Published - 15 Oct 2012 |
Keywords
- Absolute norm
- Köthe space
- Numerical index
- Polynomial
- Unconditional basis