Abstract
Using elementary properties of coalgebras, a limit theorem for linear functionals on a coalgebra is proved which generalizes several non-commutative central limit theorems [3, 5, 6, 9].
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References
Abe, E.: Hopf Algebras, Cambridge University Press (1980)
Bourbaki, N.: Elements of Mathematics, Algebra, Chap. III, Hermann, Paris (1973)
Canisius, J.: Algebraische Grenzwertsätze und unbegrenzt teilbare Funktionale, Diplomarbeit, Heidelberg (1979)
Chung, K. L.: A Course in Probability Theory, Harcourt, Brace and World, New York (1968)
Giri, N. and von Waldenfels, W.: An Algebraic Version of the Central Limit Theorem, Z. Wahrscheinlichkeitstheorie verw. Gebiete 42, 129–134 (1978)
Hudson, R. L.: A Quantum-Mechanical Central Limit Theorem for Anti-Commuting Observables, J. Appl. Prob. 10, 502–509 (1973)
Schürmann, M.: Positive and Conditionally Positive Linear Functionals on Coalgebras, in Lect. Notes in Math. 1136, Springer, New York, Heidelberg, Berlin, 475–492 (1985)
Sweedler, M. E.: Hopf Algebras, Benjamin, New York (1969)
von Waldenfels, W.: An Algebraic Central Limit Theorem in the Anticommuting Case, Z. Wahrscheinlichkeitstheorie verw, Gebiete 42, 135–140 (1978)
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© 1986 Springer-Verlag
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Schürmann, M. (1986). A central limit theorem for coalgebras. In: Heyer, H. (eds) Probability Measures on Groups VIII. Lecture Notes in Mathematics, vol 1210. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077181
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DOI: https://doi.org/10.1007/BFb0077181
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