논문KCI 등재
Liftings of a complemented subspace of $\mathcal{L}_1-$spaces
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
In this article, we prove that an infinite dimensional complemented subspace $X$ of $\mathcal{L}_{1}$-space $Z$ with unconditional basis $(x_n )$ has the lifting property. Hence we can give an alternative proof that $X$ is isomorphic to $\ell_1$ given by Lindenstrauss and Pelczy\'nski.
Abstract
In this article, we prove that an infinite dimensional complemented subspace $X$ of $\mathcal{L}_{1}$-space $Z$ with unconditional basis $(x_n )$ has the lifting property. Hence we can give an alternative proof that $X$ is isomorphic to $\ell_1$ given by Lindenstrauss and Pelczy\'nski.
참고문헌 (8)
- J. Diestel, "Absolutely summing operators" (1995), Cambridge Univ. Press
- A. Grothendieck, "Une caraterisation vectorielle-m´etrique L1", Canad J. Math, 7, pp.552~562 (1955)[DOI]
- G. K¨othe, "Hebbare lokakonvex Raumes", Math. Ann, 165, pp.188~195 (1993)
- W. B. Johnson, "Handbook of the Geometry of Banach Spaces, Vol. 2" (2001), Elsevier Science B.V
- J. Lindenstrauss, "On a certain subspace of `1", Bull. Pol. Sci, 12(9), pp.539~542 (1964)
- J. Lindenstrauss, "Absolutely summing operators in Lp-spaces and their applications", Studia Math, 29, pp.275~326 (1968)
- A. Pelczy´nski, "Projections in certain Banach spaces", Studia Math, 19, pp.209~228 (1960)
- G. Pisier, "Factorizations of linear operators and geometry of Banach spaces", C.B.M.S. Amer. Math.Soc, 60 (1985)
관련 논문AI추천
Liftings of absolutely summing operators on $\mathcal{L}_1^\lambda-$ spaces강정흥강원경기수학회 · 한국수학논문집2022 · 제30권 제1호Extending and lifting operators on Banach spaces강정흥강원경기수학회 · 한국수학논문집2019 · 제27권 제3호Liftable operators on some Banach Spaces강정흥강원경기수학회 · 한국수학논문집2015 · 제23권 제3호Some geometric property of Banach spaces-property (Ck)이종성, 조규근강원경기수학회 · 한국수학논문집2009 · 제17권 제3호Approximation properties of pairs of subspaces이근영대한수학회 · 대한수학회보2019 · 제56권 제3호Alternate signs (A_k) property in Banach spaces이종성, 조규근강원경기수학회 · 한국수학논문집2011 · 제19권 제3호
이 간행물의 다른 논문 (11건)
Common fixed point results via $F$-contraction on $C^{\ast}$-algebra valued metric spacesGopi Prasad, Ramesh Chandra Dimri, Shivani Kukretipp. 391-403Rings in which every semicentral idempotent is centralMuhammad Saadpp. 405-417A non-overlapping domain decomposition method for a discontinuous Galerkin method: a numerical study박은희pp. 419-431On partial solutions to conjectures for radius problems involving lemniscate of BernoulliGurpreet Kaurpp. 433-444Direct product, subdirect product, and representability in autometrized algebrasGebrie Yeshiwas Tilahun, Mulugeta Habte Melesse, Radhakrishna Kishore Parimipp. 445-463