Abstract
We establish a criterion of reflexivity for a separable Banach space in terms of the relation between the imbedding of the images, factorization, and majorization of operators acting in this space.
References
R. G. Douglas, “On majorization, factorization, and range inclusion of operators in Hilbert space,”Proc. Amer. Math. Soc.,17, No. 2, 413–415 (1966).
M. R. Embry, “Factorization on operators in Banach space,”Proc. Amer. Math. Soc.,38, No. 3, 587–590 (1973).
L. A. Lyusternik and V. I. Sobolev,Elements of Functional Analysis [in Russian], Nauka, Moscow (1965).
I. Lindenstrass and L. Tzafriri,Classical Banach Spaces. I, Springer, Berlin (1977).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 2, pp. 260–262, February, 1999.
Rights and permissions
About this article
Cite this article
Vershinin, R.V. Imbedding of the images of operators and reflexivity of Banach spaces. Ukr Math J 51, 293–296 (1999). https://doi.org/10.1007/BF02513482
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02513482