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)


A commutativity theorem for semibounded operators in hilbert space

Author: A. Edward Nussbaum
Journal: Proc. Amer. Math. Soc. 125 (1997), 3541-3545
MSC (1991): Primary 47B25
MathSciNet review: 1402881
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $A$ and $B$ be semibounded (bounded from below) operators in a Hilbert space $\mathfrak H$ and $\mathfrak D$ a dense linear manifold contained in the domains of $AB$, $BA$, $A^2$, and $B^2$, and such that $ABx=BAx$ for all $x$ in $\mathfrak D$. It is shown that if the restriction of $(A+B)^2$ to $\mathfrak D$ is essentially self-adjoint, then $A$ and $B$ are essentially self-adjoint and $\bar A$ and $\bar B$ commute, i.e. their spectral projections permute.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47B25

Retrieve articles in all journals with MSC (1991): 47B25

Additional Information

A. Edward Nussbaum
Affiliation: Department of Mathematics, Washington University, St. Louis, Missouri 63130

PII: S 0002-9939(97)03977-4
Received by editor(s): April 30, 1996
Dedicated: Dedicated to Allen Devinatz
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 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