Vol. 18, No. 1, 1966

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 331: 1
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
Operators of Riesz type

Selwyn Ross Caradus

Vol. 18 (1966), No. 1, 61–71
Abstract

The concept of an operator of Riesz type was introduced by A. F. Ruston by using as an axiomatic system those properties of compact operator used by F. Riesz in his original discussion of integral equations. In this paper we first show that this system of axioms can be somewhat simplified, and that in fact the class of operators of Riesz type coincides with the class of bounded linear operators whose Fredholm region consists of all nonzero complex numbers. It is further shown that the class of strictly singular operators introduced by T. Kato and the class of inessential operators introduced by D. C. Kleinecke both lie within . Next, perturbation theory is considered and it is shown that with suitable commutativity conditions, has the defining properties of a closed ideal. Finally, if f is analytic on an open set containing σ(T) and f(0) = 0, then f(T) ∈ℛ if T ∈ℛ. Moreover, if T ∈ℛ, then the algebra generated by T also lies within .

Mathematical Subject Classification
Primary: 47.10
Secondary: 47.45
Milestones
Received: 26 February 1965
Published: 1 July 1966
Authors
Selwyn Ross Caradus