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BY-NC-ND 4.0 license Open Access Published by De Gruyter Open Access October 20, 2017

Two properties of Müntz spaces

  • Trond A. Abrahamsen , Aleksander Leraand , André Martiny and Olav Nygaard EMAIL logo
From the journal Demonstratio Mathematica


We show that Müntz spaces, as subspaces of C[0, 1], contain asymptotically isometric copies of c0 and that their dual spaces are octahedral.


[1] Albiac F., Kalton N., Topics in Banach Space Theory, Graduate Texts in Math., 233, Springer, 2006Search in Google Scholar

[2] Dowling P. N.„ Lennard C. J., Turett B., Asymptotically isometric copies of c0 in Banach spaces, J. Math. Anal. Appl., 1998, 219(2), 377-39110.1006/jmaa.1997.5820Search in Google Scholar

[3] James R. C., Uniformly non-square Banach spaces, Ann. of Math., 1964, 80, 542-55010.2307/1970663Search in Google Scholar

[4] Deville R., A dual characterization of the existence of small combination of slices, Bull. Austr. Math. Soc., 1988, 37(1), 113-12010.1017/S0004972700004214Search in Google Scholar

[5] Godefroy G., Metric characterizations of first Baire class linear forms and octahedral norms, Studia Math., 1989, 95(1), 1-1510.4064/sm-95-1-1-15Search in Google Scholar

[6] Becerra Guerrero J., López-Pérez G., Rueda Zoca A., Octahedral norms and convex combination of slices in Banach spaces, J. Funct. Anal., 2014, 266(4), 2424--243510.1016/j.jfa.2013.09.004Search in Google Scholar

[7] Haller R., Langemets J., Põldvere M., On duality of diameter 2 properties, J. Convex Anal., 2015, 22(2), 465-482Search in Google Scholar

[8] Harmand P., Werner D., WernerW., M-Ideals in Banach Spaces and Banach Algebras, Lecture Notes inMath., 1547, Springer, Berlin-Heidelberg-New York, 199310.1007/BFb0084355Search in Google Scholar

[9] Gurariy V., LuskyW., Geometry ofMüntz spaces and related questions, Lecture Notes inMath., 1870, Springer-Verlag, Berlin, 2005 Search in Google Scholar

[10] Petrácek P., Geometry of Müntz spaces, in WDS’12 Proceedings of Contributed Papers: Part I - Mathematics and Computer Sciences (eds. J. Safrankova and J. Pavlu), Prague, Matfyzpress, 2012, 31-35 Search in Google Scholar

[11] Dowling P. N., Johnson W. B., Lennard C. J., Turett B., The optimality of James’s distortion theorems, Proc. Amer. Math. Soc., 1997, 125(1), 167-174 10.1090/S0002-9939-97-03537-5Search in Google Scholar

[12] Abrahamsen T. A., Lima V., Nygaard O., Troyanski S., Diameter two properties, Convexity and smoothness, Milan J. Math., 2016, 84(2), 231-242 10.1007/s00032-016-0258-1Search in Google Scholar

[13] Dilworth S. J., Girardi M., Hagler J., Dual Banach spaces which contain an isometric copy of L1, Bull. Polish Acad. Sci. Math., 2000, 48(1), 1-12 Search in Google Scholar

[14] Werner D., A remark about Müntz spaces spaces, in Google Scholar

[15] Yagoub-Zidi Y., Some isometric properties of subspaces of function spaces, Mediterr. J. Math., 2013, 10, 1905-191510.1007/s00009-013-0322-9Search in Google Scholar

Received: 2017-06-14
Accepted: 2017-06-14
Published Online: 2017-10-20
Published in Print: 2017-10-26

© 2017 Olav Nygaard et al

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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