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Isometries of normed spaces

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Figiel T., Šemrl P., Väisälä J.

Colloquium Mathematicum

2002

tom 92

nr 1

153-154

We improve the Mazur-Ulam theorem by relaxing the surjectivity condition.

Selecting basic sequences in φ-stable Banach spaces

100%

Figiel T., Frankiewicz R., Komorowski R., Ryll-Nardzewski C.

Studia Mathematica

2003

tom 159

nr 3

499-515

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 basic sequences with some special properties as well as new proofs of some known results. In particular, we get a new proof of the Gowers dichotomy theorem which produces the best unconditionality constant (also in the complex case).

Ograniczanie wyników

1 Colloquium Mathematicum

1 Studia Mathematica

2 Figiel T.

1 Frankiewicz R.

1 Komorowski R.

1 Ryll-Nardzewski C.

1 Väisälä J.

1 Šemrl P.

1 2003

1 2002

Wyniki wyszukiwania

Isometries of normed spaces

Selecting basic sequences in φ-stable Banach spaces