## A note on the extension of compact operators

HTML articles powered by AMS MathViewer

- by Ȧsvald Lima PDF
- Proc. Amer. Math. Soc.
**64**(1977), 374-375 Request permission

## Abstract:

We prove that for a real Banach space*A*the following properties are equivalent: (1) For every pair

*X*,

*Y*of Banach spaces such that $X \subseteq Y$, every compact linear operator $T:X \to A$ admits an almost normpreserving extension $\tilde T:Y \to A$. (2) The same as (1) but with $\dim X = 2$ and $Y = l_\infty ^3$.

## References

- George Elliott and Israel Halperin,
*Linear normed spaces with extension property*, Canad. Math. Bull.**9**(1966), 433–441. MR**208337**, DOI 10.4153/CMB-1966-052-6 - Otte Hustad,
*Intersection properties of balls in complex Banach spaces whose duals are $L_{1}$ spaces*, Acta Math.**132**(1974), no. 3-4, 283–313. MR**388049**, DOI 10.1007/BF02392118 - Åsvald Lima,
*Intersection properties of balls and subspaces in Banach spaces*, Trans. Amer. Math. Soc.**227**(1977), 1–62. MR**430747**, DOI 10.1090/S0002-9947-1977-0430747-4 - Joram Lindenstrauss,
*Extension of compact operators*, Mem. Amer. Math. Soc.**48**(1964), 112. MR**179580**

## Additional Information

- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**64**(1977), 374-375 - MSC: Primary 47B05; Secondary 46B05
- DOI: https://doi.org/10.1090/S0002-9939-1977-0448135-9
- MathSciNet review: 0448135