A note on best approximation and invertibility of operators on uniformly convex Banach spaces
It is shown that if X is a uniformly convex Banach space and S a bounded linear operator on X for which ‖I−S‖=1, then S is invertible if and only if ‖I−12S‖<1. From this it follows that if S is invertible on X then either (i) dist(I,[S])<1, or (ii) 0 is the unique best approximation to I from...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171291000832 |