Distance between normal operators

Sunder, V. S. (1982) Distance between normal operators Proceedings of the American Mathematical Society, 84 (4). pp. 483-484. ISSN 0002-9939

PDF - Publisher Version

Official URL: http://www.ams.org/journals/proc/1982-084-04/S0002...


Lidskii and Wielandt have proved independently that if A and B are selfadjoint operators on an n-dimensional space H, with eigenvalues {αk}nk=l and {βk}nk=1 respectively (counting multiplicity), then, ||A-B||≥minσεSn||diag (αkσ(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 skew-self-adjoint.

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