Vol. 65, No. 2, 1976

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
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