# On equivalent strictly G-convex renormings of Banach spaces

Open Mathematics (2010)

- Volume: 8, Issue: 5, page 871-877
- ISSN: 2391-5455

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topNataliia Boyko. "On equivalent strictly G-convex renormings of Banach spaces." Open Mathematics 8.5 (2010): 871-877. <http://eudml.org/doc/269086>.

@article{NataliiaBoyko2010,

abstract = {We study strictly G-convex renormings and extensions of strictly G-convex norms on Banach spaces. We prove that ℓω(Γ) space cannot be strictly G-convex renormed given Γ is uncountable and G is bounded and separable.},

author = {Nataliia Boyko},

journal = {Open Mathematics},

keywords = {Strict convexity; Complex uniform convexity; Strict G-convexity; strict convexity; complex uniform convexity; strict -convexity},

language = {eng},

number = {5},

pages = {871-877},

title = {On equivalent strictly G-convex renormings of Banach spaces},

url = {http://eudml.org/doc/269086},

volume = {8},

year = {2010},

}

TY - JOUR

AU - Nataliia Boyko

TI - On equivalent strictly G-convex renormings of Banach spaces

JO - Open Mathematics

PY - 2010

VL - 8

IS - 5

SP - 871

EP - 877

AB - We study strictly G-convex renormings and extensions of strictly G-convex norms on Banach spaces. We prove that ℓω(Γ) space cannot be strictly G-convex renormed given Γ is uncountable and G is bounded and separable.

LA - eng

KW - Strict convexity; Complex uniform convexity; Strict G-convexity; strict convexity; complex uniform convexity; strict -convexity

UR - http://eudml.org/doc/269086

ER -

## References

top- [1] Boyko N., On arrangement of operators coefficients of series member, Visn. Khark. Univ., Ser. Mat. Prykl. Mat. Mekh., 2008, 826(58), 197–210, (in Russian) Zbl1164.46306
- [2] Boyko N., Kadets V., Uniform G-convexity for vector-valued L p spaces, Serdica Math. J., 2009, 35, 1–14 Zbl1224.46020
- [3] Conway J.B., A Course in Functional Analysis, 2nd ed., Graduate Texts in Mathematics, 96, Springer, New York, 1990 Zbl0706.46003
- [4] Diestel J., Geometry of Banach Spaces - Selected Topics, Lecture Notes in Mathematics, 485, Springer, New York, 1975 Zbl0307.46009
- [5] Kadets V.M., A Course in Functional Analysis. Textbook for students of mechanics and mathematics, Kharkov State University, Kharkov, 2006, (in Russian) Zbl1128.46001
- [6] Tang W.-K., On the extension of rotund norms, Manuscripta Math., 1996, 91(1), 73–82 http://dx.doi.org/10.1007/BF02567940 Zbl0868.46012

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