Vol. 18, No. 3, 1966

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Vol. 286: 1  2
Vol. 285: 1  2
Vol. 284: 1  2
Vol. 283: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Subscriptions
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Conditions implying normality in Hilbert space

Mary Rodriguez Embry

Vol. 18 (1966), No. 3, 457–460
Abstract

The problem with which this paper is concerned is that of finding new conditions which imply the normality of an operator on a complete inner product space S. Each such condition, presented in this paper, involves the commutativity of certain operators, associated with a given operator A. Theorem 1 states the equivalence of the following conditions: (i) A is normal, (ii) each of AA and AA commutes with Re A, (iii) AA commutes with Re A and AA commutes with Im A. Theorem 2 states that A is normal if AA and AA commute and Re A is nonnegative definite. Finally, Theorem 3 states that if AA commutes with each of AA and Re A, then AA commutes with A. In this case, if A is reversible, then A is normal.

Mathematical Subject Classification
Primary: 47.40
Milestones
Received: 4 June 1965
Published: 1 September 1966
Authors
Mary Rodriguez Embry