논문KCI 등재
Extending and lifting operators on Banach spaces
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
In this article, we show that the nuclear operator defined on Banach space has an extending and lifting operator. Also we give new proofs of the well known facts which were given Pelcz\'ynski theorem for complemented subspaces of $\ell_1$ and Lewis and Stegall's theorem for complemented subspaces of $L_1(\mu)$.
Abstract
In this article, we show that the nuclear operator defined on Banach space has an extending and lifting operator. Also we give new proofs of the well known facts which were given Pelcz\'ynski theorem for complemented subspaces of $\ell_1$ and Lewis and Stegall's theorem for complemented subspaces of $L_1(\mu)$.
참고문헌 (19)
- J. Diestel, "Absolutely summing operators, Vol. 43" (1995), Cambridge University Press
- J. Diestel, "Vector Measures", Math. Surveys Monographs, 15
- A. Grothendieck, "Une caraterisation vectorielle-metrique L1", Canad J. Math, 7, pp.552~562 (1955)[DOI]
- W.B. Johnson, "Handbook of the Geometry of Banach Spaces, Vol. 2" (2001), Elsevier Science B.V
- W.B. Johnson, "Extension of operators from subspaces of c0(Γ) into C(K) space", Proc. Amer. Math. Soc, 107, pp.751~754 (1989)
- J. H. Kang, "Lifting properties on L1(Γ)", Comm. Korean Math, 16(1), pp.119~124 (2001)
- 강정흥, "Liftable operators on some Banach Spaces", 한국수학논문집, 23(3), pp.447~456 (2015), 강원경기수학회[DOI]
- J.H. Kang, "Lifting on G.T. Banach Spaces with unconditional basis", International J. Math. Analysis, 10(14), pp.677~686 (2016)
- G. Kothe, "Hebbare lokakonvex Raume", Math. Ann., 4651(165), pp.188~195 (1993)
- D. R. Lewis, "Banach spaces whose duals are isomorphic to ℓ1(Γ)", J. Functional Analysis, 12, pp.177~187 (1973)
- J. Lindenstrauss, "A remark on ℓ1 spaces", Israel J. Math, 8, pp.80~82 (1970)
- J. Lindenstrauss, "Contributions to the theory of classical Ba-nach spaces", J. Funct. Anal, 8, pp.225~249 (1971)
- J. Lindenstrauss, "Classical Banach Spaces I" (1977), Springer-Verlag
- B. Maurey, "Un theorem de prolongement", C. R. Acad. Sci. Paris A, 279, pp.329~332 (1974)
- E. Michael, "Continuous selections", Ann. of Math, 63, pp.361~382 (1956)
- L. Nachbin, "A theorem of Hahn-Banach type for linear tranformation", Trans. Amer. Math. Soc, 68, pp.28~46 (1950)
- A. Pelczynski, "Projections in certain Banach spaces", StudiaMath, 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)
- M. Zippin, "Applications of E. Michael's continuous selection theorem to operator extension problems", Proc. Amer. Soc, 127 (1999)
관련 논문AI추천
Liftings of a complemented subspace of $\mathcal{L}_1-$spaces강정흥강원경기수학회 · 한국수학논문집2023 · 제31권 제4호Liftings of absolutely summing operators on $\mathcal{L}_1^\lambda-$ spaces강정흥강원경기수학회 · 한국수학논문집2022 · 제30권 제1호Liftable operators on some Banach Spaces강정흥강원경기수학회 · 한국수학논문집2015 · 제23권 제3호The ideal of weakly $p$-nuclear operators and its injective and surjective hulls김주명대한수학회 · 대한수학회지2019 · 제56권 제1호Approximation properties of pairs of subspaces이근영대한수학회 · 대한수학회보2019 · 제56권 제3호Extreme points of the space ${\mathcal L}(^2l_{\infty})$김성권대한수학회 · 대한수학회논문집2020 · 제35권 제3호
이 간행물의 다른 논문 (17건)
On strong metric dimension of zero-divisor graphs of ringsM. Imran Bhat, SHARIEFUDDIN PIRZADApp. 563-580Some applications for generalized fractional operators in analytic functions spacesAdem Kilicman, Zainab E. Abdulnabypp. 581-594$\beta$-fuzzy filters in MS-algebrasBerhanu Assaye Alaba, Teferi Getachew Alemayehupp. 595-612Edge Szeged indices of Benzene ringMuhammad Mushtaq, Abdul Qudair Baig, Wei Gao, Muhammad Naeempp. 613-627Common fixed point results for non-compatible R-weakly commuting mappings in probabilistic semimetric spaces using control functionsKrishnapada Daspp. 629-643