PROXIMINALITY OF CERTAIN SPACES OF COMPACT OPERATORS

• Published : 2001.02.01

Abstract

For any closed subspace X of $\ell_p, \; 1<\kappa<\infty$, K(X) is proximinal in L(X), and if X is a Banach space with an unconditional shrinking basis, then K(X, c$_0$) is proximinal in L(X,$\ell_\infty$).

References

1. Ann. of Math. v.96 Structure in real Banach spaces E.M.Alfsen;E.G.Effros
2. Ann. of Math. v.109 no.2 Approximation by compact operators and the space H? + C S.Axler;I.D.Berg;N.Jewell;A.Shields
3. Trans. Amer. Math. Soc. v.261 The Essential norm of an operator and its adjoint
4. Israel J. of Math. v.51 An operator in L? Without Best Compact Approximation Y.Beyamini;P.K. Lin
5. Canad. Math. Bull. v.32 A Note on M-ideals of Compact Operators C.M.Cho
6. J. of Approximation Theory v.29 On a certain subset of L₁(0, 1) and non-existence of best approximation in some subspaces of operators M.Feder
7. Rev. Roum. Math. Puer et Appl. v.6 Characterization of proximinal Subspaces in Normed Linear Spaces G.Godini
8. Duke Math. J. v.42 Approximation from the space of compact operators and other M-ideals R.B.Holmes;B.Scranton;J.Ward
9. Proc. Amer. Math. Soc. v.123 Best Approximation in L?(I, X) R.Khalii;F.Saidi
10. Trans. Amer. Math. Soc. v.227 Intersection properties of balls and subspaces of Banach spaces A.Lima
11. Math. Scand. v.44 M-ideals of compact operators in classical Banach spaces
12. Trans. Amer. Math. Soc. v.95 Uniqueness of Hahn-Banach extensions and unique best approximation R.Philps
13. Math. Ann v.250 Best Approximation in the Space of Bounded Operators and its Applications K.Saatkamp
14. J. Func. Anal. v.27 M-ideal structure in Banach algebras R.Smith;J.Ward
15. Bull. Austral. math. Soc. v.20 Best Approximation and Intersections of balls in banach spaces D.T.Yost
16. J.Approximation Theory v.49 Approximation by Compact Operators between C(X) Spaces