Isometries of complex symmetric sequence spaces
type: Item
instance of: scholarly article
title: Isometries of complex symmetric sequence spaces
zbMATH Open document ID: 0538.47017
DOI: 10.1007/BF01159187
author: Jonathan Arazy
published in: Mathematische Zeitschrift
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173550
review text: Let E be a symmetric sequence space over the complex scalars. Then (I) Every bounded Hermitian operator on E is of the form \(T(x_ k)=(a_ k x_ k),\) where \((a_ k)\) is a real, bounded sequence; (II) Every isometry V of E onto itself is of the form \(V(x_ k)=(\lambda_ k x_{\pi(k)}),\) where \((\lambda_ k)\) are unimodular scalars and \(\pi\) is a permutation of the positive integers.
Mathematics Subject Classification ID: 47B37
Mathematics Subject Classification ID: 46A45
zbMATH DE Number: 3855807
zbMATH Keywords: symmetric sequence space
zbMATH Keywords: bounded Hermitian operator
MaRDI profile type: Publication
cites work: Q4107068
cites work: Q4136031
cites work: Q5633092
cites work: Isometries of norm ideals of compact operators
OpenAlex ID: W2045594884
description: scientific article; zbMATH DE number 3855807