An operator on \(L^ p\) without best compact approximation
type: Item
instance of: scholarly article
title: An operator on \(L^ p\) without best compact approximation
zbMATH Open document ID: 0596.47020
DOI: 10.1007/BF02764722
author: Yoav Benyamini
author: Pei-Kee Lin
published in: Israel Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: The authors show the validity of the following two theorems: Theorem 1. For every \(1\leq p\leq \infty\), \(p\neq 2\), there is an operator on \(L^ p\) whose distance to the compact operators on \(L^ p\) is not attained; (the novelty is for the cases \(1<p<\infty\) with \(p\neq 2)\) and Theorem 2. Fix \(p\neq 1,2,\infty\). For each \(\epsilon >0\) there is \(\delta (\epsilon)>0\) so that if \(K\in K(L^ p)\) and \(\| K\| >\epsilon\), then \(\| I-K\| \geq 1+\delta (\epsilon)\); (also the zero operator on \(L^ p\) is the unique best compact approximation of the identity operator I).
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 41A35
zbMATH DE Number: 3960340
zbMATH Keywords: operator on \(L^ p\)
zbMATH Keywords: distance
zbMATH Keywords: compact operators
zbMATH Keywords: best compact approximation of the identity operator
reviewed by: I. Gottlieb
MaRDI profile type: Publication
cites work: Approximation by compact operators and the space \(H^\infty +C\)
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description: scientific article; zbMATH DE number 3960340