Vol. 52, No. 2, 1974

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Some convergence theorems in Banach algebras

J. J. Koliha

Vol. 52 (1974), No. 2, 467–473
Abstract

This paper is concerned with finding necessary and sufficient conditions for the convergence of the sequence {fn(a)} of elements of Banach algebra, where {fn} is a sequence of analytic functions imitating the behavior of the sequence of integral powers. In particular, it is shown that the sequence {an} converges iff the spectrum of a (with the possible exception of the point λ = 1) lies in the open unit disc and λ = 1 is a pole of (λ a)1 of order 1.

Mathematical Subject Classification 2000
Primary: 46H05
Milestones
Received: 7 August 1973
Revised: 28 November 1973
Published: 1 June 1974
Authors
J. J. Koliha