Open Access
August, 1977 Pointwise Convergence Theorems for Self-Adjoint and Unitary Contractions
Richard Duncan
Ann. Probab. 5(4): 622-626 (August, 1977). DOI: 10.1214/aop/1176995773


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.


Download Citation

Richard Duncan. "Pointwise Convergence Theorems for Self-Adjoint and Unitary Contractions." Ann. Probab. 5 (4) 622 - 626, August, 1977.


Published: August, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0368.40001
MathSciNet: MR444901
Digital Object Identifier: 10.1214/aop/1176995773

Primary: 40A05
Secondary: 28A20

Keywords: $L^p(\mu)$-contraction , a.e. convergence , orthogonal projection

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 4 • August, 1977
Back to Top