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Tight extensions of normed spaces
Author:
N. V. Rao
Journal:
Proc. Amer. Math. Soc. 118 (1993), 641-644
MSC:
Primary 46B20; Secondary 54D35, 54E35
MathSciNet review:
1152288
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Abstract: In this note we show that bound extensions as defined by Kaufman (Acta Univ. (Szeged) 21 (1966), 163) and tight extensions as defined by Dress (Adv. in Math. 53 (1984), 322) are the same. Further we find that the property of being a bound extension is preserved under complexification.
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Andreas
W. M. Dress, Trees, tight extensions of metric spaces, and the
cohomological dimension of certain groups: a note on combinatorial
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Soc. 70 (1964),
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R.
Kaufman, A type of extension of Banbach spaces, Acta Sci.
Math. (Szeged) 27 (1966), 163–166. MR 0205037
(34 #4872)
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Leopoldo
Nachbin, A theorem of the Hahn-Banach type for
linear transformations, Trans. Amer. Math.
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V. Rao, The metric injective hulls of normed spaces, Topology
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- [1]
- Henry B. Cohen, Injective envelopes of Banach spaces, Bull. Amer. Math. Soc. 70 (1964), 723-726. MR 0184060 (32:1536)
- [2]
- A. W. M. Dress, Trees, tight extension of metric spaces, and the cohomological dimension of certain groups: a note on combinatorial properties of metric spaces, Adv. in Math. 53 (1984), 321-402. MR 753872 (86j:05053)
- [3]
- J. R. Isbell, Six theorems about injective metric spaces, Comment. Math. Helv. 39 (1964/1965), 65-74. MR 0182949 (32:431)
- [4]
- -, Injective envelopes of Banach spaces are rigidly attached, Bull. Amer. Math. Soc. 70 (1964), 727-729. MR 0184061 (32:1537)
- [5]
- R. Kaufman, A type of extension of Banach spaces, Acta Univ. (Szeged) 21 (1966), 163-166. MR 0205037 (34:4872)
- [6]
- Leopoldo Nachbin, Banach spaces with extension property, Trans. Amer. Math. Soc. 68 (1950), 28-46. MR 0032932 (11:369a)
- [7]
- N. V. Rao, The metric injective hulls of normed spaces, Topology Appl. (to appear). MR 1177160 (93h:46104)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1993-1152288-6
PII:
S 0002-9939(1993)1152288-6
Article copyright:
© Copyright 1993 American Mathematical Society
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