Vol. 19, No. 3, 1966

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
The spectral theorem for unbounded normal operators

S. J. Bernau

Vol. 19 (1966), No. 3, 391–406
Abstract

This paper gives a direct constructive proof of the spectral theorem for a normal operator T (bounded or unbounded) in a complex Hilbert space. It depends on the results, recently obtained by elementary methods, that an unbounded positive self adjoint operator A has a unique positive self adjoint square root A12; and an arbitrary self adjoint operator A has a unique representation A = A+ A with A+ and A self adjoint and positive and the range of each contained in the null space of the other.

Mathematical Subject Classification
Primary: 46.30
Milestones
Received: 4 November 1965
Published: 1 December 1966
Authors
S. J. Bernau