KADEC-KLEE PROPERTIES FOR L(`p, `q)
نویسنده
چکیده
It is proved that L(`p, `q) has the KK property if and only if it has the UKK property if and only if 1 < q < 2 < p < ∞. It is also proved that L(c0, `1) has the UKK property and that L(c0, `q) can be renormed to have the weak-star UKK property if (and only if) 1 ≤ q < 2. In all other cases L(`p, `q) has no equivalent UKK norm. Finally, it is proved that none of these spaces is either strictly convex or uniformly convexifiable. Denka Kutzarova was supported in part by the Bulgarian Ministry of Education and Science under contract MM-213/92
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