Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Commutator approximants


Author: P. J. Maher
Journal: Proc. Amer. Math. Soc. 115 (1992), 995-1000
MSC: Primary 47B47; Secondary 47A30, 47B10, 47B15
MathSciNet review: 1086335
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper deals with minimizing $ \vert\vert B - (AX - XA)\vert{\vert _p}$, where $ A$ and $ B$ are fixed, $ B \in {\mathcal{C}_p}$, and $ X$ varies such that $ AX - XA \in {\mathcal{C}_p}$. (Here, $ {\mathcal{C}_p}$ denotes the von Neumann-Schatten class and $ {\left\Vert \right\Vert _p}$ denotes its norm.) The main result (Theorem 3.2) says that if $ A$ is normal and $ AB = BA$ then $ \vert\vert B - (AX - XA)\vert{\vert _p},1 \leq p < \infty $, is minimized if and for $ 1 < p < \infty $ only if, $ AX - XA = 0$; and that the map $ X \to \vert\vert B - (AX - XA)\vert\vert _p^p,1 < p < \infty $, has a critical point at $ X = V$ if and only if $ AV - VA = 0$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B47, 47A30, 47B10, 47B15

Retrieve articles in all journals with MSC: 47B47, 47A30, 47B10, 47B15


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1086335-6
PII: S 0002-9939(1992)1086335-6
Keywords: Commutator, von Neumann-Schatten class, Fuglede's theorem, functional calculus
Article copyright: © Copyright 1992 American Mathematical Society