Abstract
We study the property of asymptotic midpoint uniform convexity for
infinite direct sums of Banach spaces, where the norm of the sum is
defined by a Banach space E with a 1-unconditional basis. We show that
a sum (∑∞n=1 Xn)E is asymptotically midpoint uniformly convex (AMUC) if
and only if the spaces Xn are uniformly AMUC and E is uniformly monotone.
We also show that Lp(X) is AMUC if and only if X is uniformly convex.
infinite direct sums of Banach spaces, where the norm of the sum is
defined by a Banach space E with a 1-unconditional basis. We show that
a sum (∑∞n=1 Xn)E is asymptotically midpoint uniformly convex (AMUC) if
and only if the spaces Xn are uniformly AMUC and E is uniformly monotone.
We also show that Lp(X) is AMUC if and only if X is uniformly convex.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 439-446 |
| Number of pages | 8 |
| Journal | Bulletin of the Belgian Mathematical Society - Simon Stevin |
| Volume | 24 |
| Issue number | 3 |
| State | Published - 2017 |