Real renormings on complex Banach spaces

Francisco J. García-Pacheco; Alejandro Miralles

doi:10.1007/s11401-007-0179-y

Chinese Annals of Mathematics, Series B ›› 2008, Vol. 29 ›› Issue (3) : 239 -246. DOI: 10.1007/s11401-007-0179-y

Article

Real renormings on complex Banach spaces

Francisco J. García-Pacheco ¹^,^a
, Alejandro Miralles ²

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Abstract

The authors prove that every complex Banach space admits an equivalent real norm that is far away from being a complex norm. Furthermore, this real norm can be chosen to share many properties with complex norms, but it is still not a complex norm.

Keywords

Complex norms / Real norms / Hilbert space

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Francisco J. García-Pacheco, Alejandro Miralles. Real renormings on complex Banach spaces. Chinese Annals of Mathematics, Series B, 2008, 29(3): 239-246 DOI:10.1007/s11401-007-0179-y

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References

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[2]	Megginson R. E.. An Introduction to Banach Space Theory, 1998, New York: Springer-Verlag

[3]	Acosta M. D., Aizpuru A., Aron R. M., García-Pacheco F. J.. Functionals that do not attain their norm. Bull. Belg. Math. Soc. Simon Stevin, 2007, 14: 407-418