The n-ball properties in real and complex Banach spaces.
Banach spaces isomorphic to proper M-ideals
contains every two-dimensional normed space
The Johnson-Lindenstrauss space.
Asplund spaces for beginners
A universal modulus for normed spaces
We define a handy new modulus for normed spaces. More precisely, given any normed space X, we define in a canonical way a function ξ:[0,1)→ ℝ which depends only on the two-dimensional subspaces of X. We show that this function is strictly increasing and convex, and that its behaviour is intimately connected with the geometry of X. In particular, ξ tells us whether or not X is uniformly smooth, uniformly convex, uniformly non-square or an inner product space.
Complemented and uncomplemented subspaces of Banach spaces.
Does a given Banach space have any non-trivial complemented subspaces? Usually, the answer is: yes, quite a lot. Sometimes the answer is: no, none at all.
Sobczyk's theorems from A to B.
Sobczyk's theorem is usually stated as: . Nevertheless, our understanding is not complete until we also recall: . Now the limits of the phenomenon are set: although c is complemented in separable superspaces, it is not necessarily complemented in a non-separable superspace, such as l.
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