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Prime Banach Space


A Banach space X is called prime if each infinite-dimensional complemented subspace of X is isomorphic to X (Lindenstrauss and Tzafriri 1977).

Pełczyński (1960) proved that c_ degrees (the Banach space of all complex sequences converging to zero together with the supremum norm) and l^p for 1<=p<infty (the space of all complex sequences {x_n} such that sum_(n=1)^(infty)|x_n|^p<infty) are prime. The L-infinity-space l^infty of all bounded complex sequences is also prime (Lindenstrauss 1967).


See also

Banach Space, Complemented Subspace

This entry contributed by Mohammad Sal Moslehian

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References

Lindenstrauss, J. "On Complemented Subspaces of m." Israel J. Math. 5, 153-156, 1967.Lindenstrauss, J. and Tzafriri, L. Classical Banach Spaces. I. Sequence Spaces. New York: Springer-Verlag, 1977.Pełczyński, A. "Projections in Certain Banach Spaces." Studia Math. 19, 209-228, 1960.

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Prime Banach Space

Cite this as:

Moslehian, Mohammad Sal. "Prime Banach Space." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/PrimeBanachSpace.html

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