A Natural Class of Sequential Banach Spaces

• Autorzy: Talponen J.

Identyfikatory

DOI

10.4064/ba59-2-8

• Języki publikacji: EN

Abstrakty

EN

We introduce and study a natural class of variable exponent ℓ^p spaces, which generalizes the classical spaces ℓ^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.

Słowa kluczowe

EN

variable exponent; Lp spaces; Banach spaces; universal spaces

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2011
• Tom: Vol. 59, no 2
• Strony: 185--196
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Talponen J.

• Aalto University, Mathematics P.O. Box 11100, FI-00076 Aalto, Finland

Bibliografia

• [1] M. Fabian, P. Habala, P. Hájek, V. Montesinos Santalucia, J. Pelant and V. Zizler, Functional Analysis and Infinite-Dimensional Geometry, CMS Books Math. 8, Springer, New York, 2001.
• [2] R. Haydon, Trees in renorming theory, Proc. London Math. Soc. 78 (1999), 541–585.
• [3] W. Johnson and J. Lindenstrauss (eds.), Handbook of the Geometry of Banach Spaces, Vol. I, North-Holland, Amsterdam, 2001.
• [4] K. Kunen and H. Rosenthal, Martingale proofs of some geometric results in Banach spaces, Pacific J. Math. 100 (1982), 153–175.
• [5] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces. I. Sequence Spaces, Ergeb. Math. Grenzgeb. 92, Springer, Berlin, 1977.
• [6] —, —, Classical Banach Spaces. II. Function Spaces, Ergeb. Math. Grenzgeb. 97, Springer, Berlin, 1979.
• [7] A. Pełczynski, Universal bases, Studia Math. 32 (1969), 247–268.
• [8] G. Pisier, Factorization of Linear Operators and Geometry of Banach Spaces, CBMS Reg. Conf. Ser. Math. 60, Amer. Math. Soc., 1986.