Abstract
The aim of this paper is to give a spectral representation for random measures of Gleason type. Random Gleason measures may be treated as a non-commutative version of stochastic processes with independent increments. Theorems 1 and 2 give the representation of such processes in terms of S-operator families. In particular, the operator-valued measure N (Theorem 2) plays the same role as the Lévy-Khinchine spectral measure in the theory of infinitely divisible distributions and it is a very convenient tool in consideration concerning convergence and compactness of sequences of random Gleason measures.
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References
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© 1977 ACADEMIA, Publishing House of the Czechoslovak Academy of Sciences, Prague
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Hensz, E., Jajte, R. (1977). Random Measures of Gleason Type. In: Kožešnik, J. (eds) Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and of the 1974 European Meeting of Statisticians. Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and of the 1974 European Meeting of Statisticians, vol 7A. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9910-3_24
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DOI: https://doi.org/10.1007/978-94-010-9910-3_24
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-9912-7
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