The Annals of Probability

Pointwise Convergence Theorems for Self-Adjoint and Unitary Contractions

Richard Duncan

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 40A05: Convergence and divergence of series and sequences
Secondary: 28A20: Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence

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

Citation

Duncan, Richard. Pointwise Convergence Theorems for Self-Adjoint and Unitary Contractions. Ann. Probab. 5 (1977), no. 4, 622--626. doi:10.1214/aop/1176995773. https://projecteuclid.org/euclid.aop/1176995773


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