A note on best approximation and invertibility of operators on uniformly convex Banach spaces

Holub, James R.

A note on best approximation and invertibility of operators on uniformly convex Banach spaces

dc.contributor.author	Holub, James R.	en
dc.contributor.department	Mathematics	en
dc.date.accessioned	2019-05-20T11:50:23Z	en
dc.date.available	2019-05-20T11:50:23Z	en
dc.date.issued	1991-01-01	en
dc.date.updated	2019-05-20T10:37:52Z	en
dc.description.abstract	It is shown that if X is a uniformly convex Banach space and S a bounded linear operator onX for which ?I-S?=1, then S is invertible if and only if ?I-12S? <1. From this it follows thatif S is invertible on X then either (i) dist(I,[S])<1, or (ii) 0 is the unique best approximation toI from [S], a natural (partial) converse to the well-known sufficient condition for invertibility thatdist(I,[S])<1.	en
dc.description.version	Published version	en
dc.format.mimetype	application/pdf	en
dc.identifier.citation	James R. Holub, "A note on best approximation and invertibility of operators on uniformly convex Banach spaces," International Journal of Mathematics and Mathematical Sciences, vol. 14, no. 3, pp. 611-614, 1991. doi:10.1155/S0161171291000832	en
dc.identifier.doi	https://doi.org/10.1155/S0161171291000832	en
dc.identifier.uri	http://hdl.handle.net/10919/89574	en
dc.language.iso	en	en
dc.publisher	Hindawi Publishing Corp	en
dc.rights	Creative Commons Attribution 4.0 International	en
dc.rights.holder	Copyright © 1991 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.	en
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/	en
dc.title	A note on best approximation and invertibility of operators on uniformly convex Banach spaces	en
dc.title.serial	International Journal of Mathematics and Mathematical Sciences	en
dc.type	Article - Refereed	en
dc.type.dcmitype	Text	en