A Cheney and Wulbert type lifting theorem in optimization

Rao, T. S. S. R. K. (2017) A Cheney and Wulbert type lifting theorem in optimization Bollettino dell'Unione Matematica Italiana, 10 (4). pp. 585-589. ISSN 1972-6724

Full text not available from this repository.

Official URL: https://link.springer.com/article/10.1007/s40574-0...


In this paper we exhibit new classes of Banach spaces for which strong notions of optimization can be lifted from quotient spaces. Motivated by a well known result of Cheney and Wulbert on lifting of proximinality from a quotient space to a subspace, for closed subspaces, Z⊂Y⊂X, we consider stronger forms of optimization, that Z has in X and the quotient space Y / Z has in X / Z should lead to the conclusion Y has the same property in X. The versions we consider have been studied under various names in the literature as L-proximinal subspaces or subspaces that have the strong-112-ball property. We give an example where the strong-112-ball property fails to lift to the quotient. We show that if every M-ideal in Y is a M-summand, for a finite codimensional subspace Z⊂Y, that is a M-ideal in X with the strong-112-ball property in X and if Y / Z has the 112-ball property in X / Z, then Y has the strong-112-ball property in X.

Item Type:Article
Source:Copyright of this article belongs to Springer Verlag.
Keywords:L-proximinality; One and Half Ball Property; Quotient Spaces
ID Code:112406
Deposited On:10 Jan 2018 04:23
Last Modified:10 Jan 2018 04:23

Repository Staff Only: item control page