Korean J. Math.  Vol 27, No 3 (2019)  pp.645-655
DOI: https://doi.org/10.11568/kjm.2019.27.3.645

Extending and lifting operators on Banach spaces

JeongHeung Kang

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 $L_1(\mu)$.

Keywords


Extension Property, lifting property, absolutely p-

Subject classification

46B03

Sponsor(s)

Korea Military Academy

Full Text:

PDF

References


J. Diestel, H. Jarchow and A. Tonge, Absolutely summing operators, Vol. 43. Cambridge University Press, 1995. (Google Scholar)

J. Diestel and J. J. Uhl. Jr, Vector Measures, Math. Surveys Monographs 15, AMS, Providence RI. (Google Scholar)

A. Grothendieck, Une caraterisation vectorielle-m ́etrique L1, Canad J. Math. 7(1955), 552–562 MR17. (Google Scholar)

W.B. Johnson and J. Lindenstrauss, Handbook of the Geometry of Banach Spaces, Vol. 2, Elsevier Science B.V. (2001). (Google Scholar)

W.B. Johnson and M. Zippin, Extension of operators from subspaces of c0(Γ) into C(K) space, Proc. Amer. Math. Soc. 107 (1989), 751–754. (Google Scholar)

J.H. Kang, Lifting properties on L1(μ), Comm. Korean Math. 16 (1) (2001), 119–124. (Google Scholar)

J.H. Kang, Lifting operators on some Banach spaces, Korean, J. Math. 23 (3) (2015), 447–456. (Google Scholar)

J.H. Kang, Lifting on G.T. Banach Spaces with unconditional basis, International J. Math. Analysis, 10 (14) (2016), 677–686. (Google Scholar)

G. K ̈othe, Hebbare lokakonvex Raume , Math. Ann., 4651. 165 (1993), 188–195. [10] D. R. Lewis and C. Stegall, Banach spaces whose duals are isomorphic to l1(Γ), J. Functional Analysis 12 (1973), 177–187. (Google Scholar)

J. Lindenstrauss, A remark on l1 spaces, Israel J. Math. 8 (1970), 80–82. (Google Scholar)

J. Lindenstrauss and A. Pelczyn ́ski, Contributions to the theory of classical Banach spaces, J. Funct. Anal. 8 (1971), 225–249. (Google Scholar)

J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I,, Springer-Verlag, Berlin and New York 1977. (Google Scholar)

B. Maurey, Un theorem de prolongement, C.R. Acad. Sci. Paris A 279 (1974), 329–332. (Google Scholar)

E. Michael, Continuous selections, Ann. of Math. 63 (1956), 361–382. (Google Scholar)

L. Nachbin, A theorem of Hahn-Banach type for linear tranformation, Trans. Amer. Math. Soc. 68 (1950), 28–46. (Google Scholar)

A. Pelczynski, Projections in certain Banach spaces, Studia Math. Vol. 19 (1960), 209-228. (Google Scholar)

G. Pisier, Factorizations of linear operators and geometry of Banach spaces, C.B.M.S. Amer. Math. Soc. 60 (1985). (Google Scholar)

M. Zippin, Applications of E. Michael’s continuous selection theorem to operator extension problems, Proc. Amer. Soc. 127 (1999). (Google Scholar)


Refbacks

  • There are currently no refbacks.


ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr