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

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Positive approximants


Author: Richard Bouldin
Journal: Trans. Amer. Math. Soc. 177 (1973), 391-403
MSC: Primary 47A65; Secondary 41A65
MathSciNet review: 0317082
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ T = B + iC$ with $ B = {B^\ast},C = {C^\ast}$ and let $ \delta (T)$ denote the the distance of T to the set of nonnegative operators. We find upper and lower bounds for $ \delta (T)$. We prove that if P is any best approximation for T among nonnegative operators then $ P \leq B + {({(\delta (T))^2} - {C^2})^{{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}}$. Provided $ B \geq 0$ or T is normal we characterize those T which have a unique best approximation among the nonnegative operators. If T is normal we characterize its best approximating nonnegative operators which commute with it. We characterize those T for which the zero operator is the best approximating nonnegative operator.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 47A65, 41A65

Retrieve articles in all journals with MSC: 47A65, 41A65


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0317082-6
PII: S 0002-9947(1973)0317082-6
Article copyright: © Copyright 1973 American Mathematical Society