The numerical range of a tridiagonal operator
type: Item
instance of: scholarly article
title: The numerical range of a tridiagonal operator
zbMATH Open document ID: 1205.47007
author: Mao-Ting Chien
author: Hiroshi Nakazato
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-10-22T00:00:00Z
review text: The authors study the numerical range of several (infinite or finite) tridiagonal matrices. As a sample, we mention here the tridiagonal operator defined by \(Ae_j = e_{j-1} + r^je_{j+1}\), with respect to the standard orthonormal basis \(\{e_n\}\) of \(\ell^2(\mathbb N)\). Such tridiagonal operators are related to some Rogers-Ramanujan identities.
Mathematics Subject Classification ID: 47A12
zbMATH DE Number: 5804462
zbMATH Keywords: numerical range
zbMATH Keywords: tridiagonal operator
zbMATH Keywords: Rogers-Ramanujan identities
reviewed by: Cătălin Badea
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.07.025
OpenAlex ID: W2043534659
cites work: Q3996250
cites work: On geometric properties of the numerical range
cites work: The numerical radius of a weighted shift operator with geometric weights
cites work: Über den Wertevorrat einer Matrix
cites work: The Numerical Range of a Weighted Shift
DOI: 10.1016/J.JMAA.2010.07.025
description: scientific article; zbMATH DE number 5804462