On the bounded approximation property on subspaces of lp when 0 < p < 1 and related issues

被引：4
作者：
Cabello Sanchez, Felix [1 ]
Castillo, Jesus M. F. [1 ]
Moreno, Yolanda [2 ]
机构：
[1] Univ Extremadura, Inst Matemat, Ave Elvas S-N, E-06071 Badajoz, Spain
[2] Univ Extremadura, Inst Matemat, Escuela Politecn, Ave Elvas S-N, E-06071 Caceres, Spain
来源：
FORUM MATHEMATICUM | 2019年 / 31卷 / 06期
关键词：
Bounded approximation property; quasi-Banach space; complementably universal; Fraisse limit; BANACH-SPACES; UNIVERSAL BASES;
D O I：
10.1515/forum-2018-0174
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper studies the bounded approximation property (BAP) in quasi-Banach spaces. In the first part of the paper, we show that the kernel of any surjective operator l(p) -> X has the BAP when X has it and 0 < p <= 1, which is an analogue of the corresponding result of Lusky for Banach spaces. We then obtain and study nonlocally convex versions of the Kadec-Pelczyfisld-Wojtaszczyk complementably universal spaces for Banach spaces with the BAP.
引用
收藏
页码：1533 / 1556
页数：24
相关论文
共 26 条
[1]  
Aviles A., 2016, Lecture Notes in Mathematics, V2132
[2]  
Cabello Sanchez F., 1998, MATH P R IR ACAD A, V98A, P121
[3]  
Casazza PG, 2001, HANDBOOK OF THE GEOMETRY OF BANACH SPACES, VOL 1, P271, DOI 10.1016/S1874-5849(01)80009-7
[4]  
Castillo J. M. F., 2017, PREPRINT
[5]   ON THE BOUNDED APPROXIMATION PROPERTY IN BANACH SPACES [J].
Castillo, Jesus M. F. ;
Moreno, Yolanda .
ISRAEL JOURNAL OF MATHEMATICS, 2013, 198 (01) :243-259
[6]   The dual form of the approximation property for a Banach space and a subspace [J].
Figiel, T. ;
Johnson, W. B. .
STUDIA MATHEMATICA, 2015, 231 (03) :287-292
[7]   Some approximation properties of Banach spaces and Banach lattices [J].
Figiel, Tadeusz ;
Johnson, William B. ;
Pelczynski, Aleksander .
ISRAEL JOURNAL OF MATHEMATICS, 2011, 183 (01) :199-231
[8]   ISOMETRIC UNIQUENESS OF A COMPLEMENTABLY UNIVERSAL BANACH SPACE FOR SCHAUDER DECOMPOSITIONS [J].
Garbulinska-Wegrzyn, Joanna .
BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 2014, 8 (01) :211-220
[9]  
Gurarii V I., 1966, Sib. Mat. Zh., V7, P1002
[10]   COMPLEMENTABLY UNIVERSAL BANACH SPACES [J].
KADEC, MI .
STUDIA MATHEMATICA, 1971, 40 (01) :85-&
123