## The Annals of Probability

### Pointwise Convergence Theorems for Self-Adjoint and Unitary Contractions

Richard Duncan

#### Abstract

Some conditions are introduced which imply pointwise convergence theorems for increasing sequences of orthogonal projections on $L^2(\mu), \mu$ finite, as well as a pointwise ergodic theorem for self-adjoint and unitary contractions. These results generalize to the case of nonpositive operators some theorems of E. M. Stein.

#### Article information

Source
Ann. Probab., Volume 5, Number 4 (1977), 622-626.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176995773

Digital Object Identifier
doi:10.1214/aop/1176995773

Mathematical Reviews number (MathSciNet)
MR444901

Zentralblatt MATH identifier
0368.40001

JSTOR