Posts by Costica Mustata

Abstract


Considering a metric space and its Lipschitz dual one defines the notion of M-ideal and HB-subspace of a metric space (with respect to its Lipschitz dual). One obtain some results analogous to these in the theory of M-ideal and HB-subspaces in a normed space. The results in the paper are based on an extension theorem of McShane [2], [3] and on a uniquenese theorem which is similar to one of R.R.Phelps [10], [11].

Authors

Costica Mustata
“Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academy, Romania

Keywords

?

Paper coordinates

C. Mustăţa, M-ideals in metric spaces, ”Babeş-Bolyai” University, Faculty of Math. and Physics, Research Seminars, Seminar on Mathematica Analysis, Preprint Nr.7 (1988), 67-74 (MR # 90b: 54019)

PDF

??

About this paper

Journal
Publisher Name
DOI
Print ISSN
Online ISSN

MR # 90b: 54019

google scholar link

[1] Alfsen, D.M., Effross, E., Structure in real Banach spaces, Ann. of Math. 96(1972), 98-173.
[2] Czisper, J.,Geher, L., Extension of Funcitons satisfying a Lipschitz conditions, Acta Math. Acad.Sci. Hungar 6(1955), 213-220.
[3] Fakhoury, E., Selections lineaires associees au Theoreme de  Hahn-Banach, J. of Funcitonal analysis 11 (1972), 436-452.
[4] Hennefeld, J., M – ideas, HB – subspaces and Compact Operators, Indiana Univ. Math. J. 28 (6) (1979), 927-934.
[5] Hennefeld, J., A note on M – ideals in B(X), Mat. Soc. 98 (1) (1980), 89-92.
[6] Holmes, R.B., Scrantor, B., Ward, J.D., Approximation from the space of compact operators and other M – ideals Duke Math. J. 42 (1975), 259-269.
[7] Holmes, R.B., Geometric Functional Analysis and its Applications, Springer – Verlag – New York – Heidelberg – Berlin, 1975.
[8] Shane, E.J., Extension of range of funcitons, Bull. Amer. Math. Soc. 40 (1934), 837-842.
[9] Johnson, J.A., Banach Spaces of Lipschitz Functions and vector – valued Lipschitz Functions, Trans. Amer. Math. Soc. 148(1970), 147-169.
[10] Mustata, C., Best Approximation and Uniwuq Extension of Lipschitz Functions, J. Approx. Theory 19 (3) (1977), 222-230.
[11] Phelps, R.R., Uniqueness of Hahn-Banach Extension and Unique Best Approximation, Trans. Amer. Math. Sec. 25 (1960), 238-255.
[12] Oja, E., On the uniquess of the norm preserving extension of linear functional in this Hahn-Banach Theorem, Proc. Acad. Science Esteonian SSR 33 (4) (1984), 422-433 (Russian).

Related Posts

M-ideals in metric spaces

Abstract Considering a metric space and its Lipschitz dual one defines the notion of M-ideal and HB-subspace of a metric…

An application of a theorem of McShane

Abstract AuthorsCostica Mustata “Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academy, Romania Keywords? Paper coordinatesC. Mustăţa, An application of a…

On a problem of extremum

Abstract AuthorsCostica Mustata “Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academy, Romania Keywords? Paper coordinatesC. Mustăţa, On a problem of…

On a contest problem

Abstract AuthorsCostica Mustata “Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academy, Romania Keywords? Paper coordinatesC. Mustăţa, On a contest problem,…

Common selections for the metric projections

Abstract AuthorsCostica Mustata “Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academy, Romania Keywords? Paper coordinatesC. Mustăţa, Common selections for the…