An example of infinite dimensional reflexive space non-isomorphic to its cartesian square
Isometries of normed spaces
We improve the Mazur-Ulam theorem by relaxing the surjectivity condition.
Selecting basic sequences in φ-stable Banach spaces
In this paper we make use of a new concept of φ-stability for Banach spaces, where φ is a function. If a Banach space X and the function φ satisfy some natural conditions, then X is saturated with subspaces that are φ-stable (cf. Lemma 2.1 and Corollary 7.8). In a φ-stable Banach space one can easily construct basic sequences which have a property P(φ) defined in terms of φ (cf. Theorem 4.5). This leads us, for appropriate functions φ, to new results on the existence of unconditional...
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