Smooth partitions of unity over Banach manifolds
type: Item
instance of: scholarly article
title: Smooth partitions of unity over Banach manifolds
zbMATH Open document ID: 0928.58011
author: O. V. Kunakovskaya
published in: Russian Mathematics
publication date: 2000-01-04T00:00:00Z
review text: The author separates out a class of Banach manifolds (in particular, Banach spaces) which admit a \(C^r\)-partition of unity \((r\geq 2)\) of a special type. The practical need to construct those special partitions of unity arises in the author's attempt to transfer the theory, developed by Yu. G. Borisovich and herself, of boundary indices of sets of generalized eigenvectors of a pair of nonlinear operators in Hilbert spaces to Banach spaces. The well-known Eells-Lang's theorem on the existence of a \(C^r\)-partition of unity for a paracompact Hausdorff \(C^r\)-manifold, where \(r \geq 1\), which is modeled by a separable Hilbert space, is deduced here as a corollary of a more general theorem (Corollary 3.2 of Theorem 3.2).
Mathematics Subject Classification ID: 58D05
Mathematics Subject Classification ID: 58C40
zbMATH DE Number: 1256814
zbMATH Keywords: partitions of unity
zbMATH Keywords: Banach manifolds
reviewed by: Neculai Papaghiuc
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1256814