Vol. 65, No. 2, 1976

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
On almost everywhere convergence of Abel means of contraction semigroups

Stephen Allan McGrath

Vol. 65 (1976), No. 2, 405–408
Abstract

Let (X,Σ) be a σ-finite measure space and Lp(X,Σ), 1 p , the usual Banach spaces of complex valued functions. Let {Tt : t 0} be a strongly continuous semigroup of contractions of Lp(X,Σ) for some 1 p < and set Rλf = 0eλtTtf dt, λ > 0. If Tt 1 for all t 0, then limλ→∞λRλf(x) = f(x) a.e. for all f Lp(X,Σ).

Mathematical Subject Classification 2000
Primary: 47D05, 47D05
Secondary: 47A20
Milestones
Received: 14 April 1976
Revised: 30 June 1976
Published: 1 August 1976
Authors
Stephen Allan McGrath