Email this article Duality and Free Measures in Vector Spaces, the Spectral Theory of Actions of Non-Locally Compact Groups
- Authors: Vershik A.M.1,2
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Affiliations:
- St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg State University
- Institute for Information Transmission Problems
- Issue: Vol 238, No 4 (2019)
- Pages: 390-405
- Section: Article
- URL: https://ogarev-online.ru/1072-3374/article/view/242537
- DOI: https://doi.org/10.1007/s10958-019-04246-5
- ID: 242537
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Abstract
The paper presents a general duality theory for vector measure spaces taking its origin in author’s papers written in the 1960s. The main result establishes a direct correspondence between the geometry of a measure in a vector space and properties of the space of measurable linear functionals on this space regarded as closed subspaces of an abstract space of measurable functions. An example of useful new features of this theory is the notion of a free measure and its applications.
About the authors
A. M. Vershik
St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg State University; Institute for Information Transmission Problems
Author for correspondence.
Email: avershik@pdmi.ras.ru
Russian Federation, St. Petersburg; Moscow
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