Tight extensions of normed spaces

Author:
N. V. Rao

Journal:
Proc. Amer. Math. Soc. **118** (1993), 641-644

MSC:
Primary 46B20; Secondary 54D35, 54E35

DOI:
https://doi.org/10.1090/S0002-9939-1993-1152288-6

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.

**[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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DOI:
https://doi.org/10.1090/S0002-9939-1993-1152288-6

Article copyright:
© Copyright 1993
American Mathematical Society