Three-Space Problems for Polynomial Properties in Banach Spaces

Arranz, F. J.; Castillo, Jesús M. F.; Carcía, Ricardo

doi:10.3318/pria.2003.103.1.39

Mathematical Proceedings of the Royal Irish Academy

2003

DOI: 10.3318/pria.2003.103.1.39

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Three-Space Problems for Polynomial Properties in Banach Spaces

F. J. Arranz¹,

Jesús M. F. Castillo²,

Ricardo Carcía³

Abstract: We study which polynomial properties are, and which are not, three-space properties.

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2021

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The positive polynomial Schur property in Banach lattices

Botelho

Luiz

2021

Proc. Amer. Math. Soc.

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We study the class of Banach lattices that are positively polynomially Schur. Plenty of examples and counterexamples are provided, lattice properties of this class are proved, arbitrary L p ( μ ) L_p(\mu ) -spaces, 1 ≤ p > ∞ 1 \leq p > \infty , are shown to be positively polynomially Schur, lattice analogues of results on Banach spaces are obtained and relationships with the positive Schur and the weak Dunford-Pettis properties are established.

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The positive polynomial Schur property in Banach lattices

Botelho

Luiz

2021

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

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Three-Space Problems for Polynomial Properties in Banach Spaces

Abstract: We study which polynomial properties are, and which are not, three-space properties.

Cited by 1 publication

References 24 publications

The positive polynomial Schur property in Banach lattices

The positive polynomial Schur property in Banach lattices

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