Sunder, V. S. (1982) Distance between normal operators Proceedings of the American Mathematical Society, 84 (4). pp. 483484. ISSN 00029939

PDF
 Publisher Version
195kB 
Official URL: http://www.ams.org/journals/proc/198208404/S0002...
Abstract
Lidskii and Wielandt have proved independently that if A and B are selfadjoint operators on an ndimensional space H, with eigenvalues {α_{k}}^{n}_{k=l} and {β_{k}}^{n}_{k=1} respectively (counting multiplicity), then, AB≥min_{σεSn}diag (α_{k}β_{σ(k)}) for any unitarily invariant norm on L(H). In this note an example is given to show that this result is no longer true if A and B are only required to be normal (even unitary). It is also shown that the above inequality holds in the operator norm, if A is selfadjoint and B is skewselfadjoint.
Item Type:  Article 

Source:  Copyright of this article belongs to American Mathematical Society. 
ID Code:  53552 
Deposited On:  09 Aug 2011 11:47 
Last Modified:  18 May 2016 06:38 
Repository Staff Only: item control page