Abstract
We study irreducible nonorthogonal resolutions of the identity. The results obtained show that, in contrast to traditional requirements of “independent measurements” type, the noncommutative approach gives a more precise description of information systems.
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References
A. S. Kholevo,Probabilistic and Statistical Aspects of Quantum Mechanics [in Russian], Nauka, Moscow (1980).
A. F. Zaritskii, “Probabilistic-operator measures in neural structures,” in:Numerical Methods of Analysis, Moscow University, Moscow (1995), pp. 105–115.
Yu. N. Bespalov, “Collections of orthoprojectors with relations,”Ukr. Mat. Zh.,44, No. 3, 309–317 (1992).
A. Yu. Piryatinskaya and Yu. S. Samoilenko, “Wild problems in the theory of representations of *-algebras generated by generatrices and relations,”Ukr. Mat. Zh.,47, No. 1, 70–78 (1995).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 12, pp. 1706–1707, December, 1995.
The author is grateful to Yu. N. Bespalov and Yu. S. Samoilenko for fruitful discussions on the theory of representations of*-algebras and useful comments.
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Zaritskii, A.F. To the mathematical theory of representation of information in neural nets. Ukr Math J 47, 1951–1952 (1995). https://doi.org/10.1007/BF01060969
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DOI: https://doi.org/10.1007/BF01060969