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A Natural Class of Sequential Banach Spaces

Jarno Talponen (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

We introduce and study a natural class of variable exponent p spaces, which generalizes the classical spaces p and c₀. These spaces will typically not be rearrangement-invariant but instead they enjoy a good local control of some geometric properties. Some geometric examples are constructed by using these spaces.

Addendum to: "Sequences of 0's and 1's" (Studia Math. 149 (2002), 75-99)

Johann Boos, Toivo Leiger (2005)

Studia Mathematica

There is a nontrivial gap in the proof of Theorem 5.2 of [2] which is one of the main results of that paper and has been applied three times (cf. [2, Theorem 5.3, (G) in Section 6, Theorem 6.4]). Till now neither the gap has been closed nor a counterexample found. The aim of this paper is to give, by means of some general results, a better understanding of the gap. The proofs that the applications hold will be given elsewhere.

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