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)


Spectral properties of linear operators for which $ T\sp*T$ and $ T$ $ +$ $ T\sp*$ commute

Authors: Stephen L. Campbell and Ralph Gellar
Journal: Proc. Amer. Math. Soc. 60 (1976), 197-202
MSC: Primary 47B20
MathSciNet review: 0417841
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The class of linear operators for which $ {T^\ast}T$ and $ T + {T^\ast}$ commute is studied. It is shown that such operators are normaloid. If T is also completely nonnormal, then $ \sigma (T) = \sigma ({T^\ast})$. Also, isolated points of $ \sigma (T)$ are reducing eigenvalues. Finally, if $ \sigma (T)$ is a subset of either a vertical line or the real axis, then T is normal.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B20

Retrieve articles in all journals with MSC: 47B20

Additional Information

PII: S 0002-9939(1976)0417841-3
Keywords: Operator such that $ {T^\ast}T$ and $ T + {T^\ast}$ commute, spectrum, normaloid operator, spectraloid operator, isoloid operator
Article copyright: © Copyright 1976 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia