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Quantitative Bessaga–Pełczyński property and quantitative Rosenthal property
Author(s) -
Chen Dongyang,
Ruan Yingbin
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800312
Subject(s) - property (philosophy) , mathematics , hausdorff space , hausdorff measure , pure mathematics , hausdorff dimension , epistemology , philosophy
We prove that c 0 and C ( K ) , where K is a dispersed compact Hausdorff space, enjoy a quantitative version of the Bessaga–Pełczyński property. We also prove that l 1 possesses a quantitative version of the Pełczyński property. Finally, we show thatL 1 ( μ )has a quantitative version of the Rosenthal property for any finite measure μ.