A note on the extension of compact operators
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- 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
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- 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