The linearity of metric projection operator for subspaces of L p spaces

Autor:	Yu. Yu. Druzhinin
Rok vydání:	2010
Předmět:	Combinatorics Discrete mathematics General Mathematics Operator (physics) Banach space Codimension Finite-rank operator Disjoint sets Compact operator Linear subspace Measure (mathematics) Mathematics
Zdroj:	Moscow University Mathematics Bulletin. 65:28-33
ISSN:	1934-8444 0027-1322
DOI:	10.3103/s0027132210010055
Popis:	Let Y be a Chebyshev subspace of a Banach space X. Then the single-valued metric projection operator PY: X ∈ Y taking each x ∈ X to the nearest element y ∈ Y is well defined. Let M be an arbitrary set and µ be a σ-finite measure on some σ-algebra Σ of subsets of M. We give a description of Chebyshev subspaces Y ⊂ Lp(M,Σ, µ) with a finite dimension and a finite codimension which the operator PY is linear for.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::8f3d29f4b200a27e9b3e22ffe4477bfd https://doi.org/10.3103/s0027132210010055 Zobrazit plný text záznamu Full text from SpringerLink