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Volumn 253, Issue 1, 2006, Pages 177-196

Remarks on the r and Δ convolutions

Author keywords

Conditionally free; Convolution; Deformations; Free and boolean convolution; Limit theorems; Moment cumulant formulae; Operator spaces

Indexed keywords


EID: 33644982355     PISSN: 00255874     EISSN: 14321823     Source Type: Journal    
DOI: 10.1007/s00209-005-0898-2     Document Type: Article
Times cited : (13)

References (33)
  • 1
    • 0000855365 scopus 로고    scopus 로고
    • Interacting Fock spaces and gaussianization of probability measures
    • [AB]
    • [AB] Accardi, L., Bożejko, M.: Interacting Fock spaces and gaussianization of probability measures. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 1(4), 663-670 (1998)
    • (1998) Infin. Dimens. Anal. Quantum Probab. Relat. Top. , vol.1 , Issue.4 , pp. 663-670
    • Accardi, L.1    Bozejko, M.2
  • 2
    • 84968491335 scopus 로고
    • Free product of C*-algebras
    • [A]
    • [A] Avitzour, D.: Free product of C*-algebras. Trans. Am. Math. Soc. 271, 423-435 (1982)
    • (1982) Trans. Am. Math. Soc. , vol.271 , pp. 423-435
    • Avitzour, D.1
  • 3
    • 0347976575 scopus 로고    scopus 로고
    • Noncommutative notions of stochastic independence
    • [BGS]
    • [BGS] Ben Ghorbal, A., Schürmann, M.: Noncommutative notions of stochastic independence. Math. Proc. Camb. Philos. Soc. 133, 531-561 (2002)
    • (2002) Math. Proc. Camb. Philos. Soc. , vol.133 , pp. 531-561
    • Ben Ghorbal, A.1    Schürmann, M.2
  • 4
    • 0348119509 scopus 로고    scopus 로고
    • Deformed Free Probability of Voiculescu
    • [B1]
    • [B1] Bożejko, M.: Deformed Free Probability of Voiculescu. RIMS Kokyuroku 1227, 96-113 (2001)
    • (2001) RIMS Kokyuroku , vol.1227 , pp. 96-113
    • Bozejko, M.1
  • 5
    • 0002548658 scopus 로고
    • Positive definite functions on free group and noncommutative Riesz product
    • [B2]
    • [B2] Bożejko, M.: Positive definite functions on free group and noncommutative Riesz product. Boll. Unione Mat. Ital. Serie VI 5 A(1), 13-21 (1986)
    • (1986) Boll. Unione Mat. Ital. Serie VI , vol.5 A , Issue.1 , pp. 13-21
    • Bozejko, M.1
  • 6
    • 0011912330 scopus 로고
    • Uniformly bounded representation of free groups
    • [B3]
    • [B3] Bożejko, M.: Uniformly bounded representation of free groups. J. Reine Angew. Math. 377, 170-186 (1987)
    • (1987) J. Reine Angew. Math. , vol.377 , pp. 170-186
    • Bozejko, M.1
  • 8
    • 0000683126 scopus 로고    scopus 로고
    • Convolution and limit theorems for conditinally free random variables
    • [BLS]
    • [BLS] Bożejko, M., Leinert, M., Speicher, R.: Convolution and limit theorems for conditinally free random variables, Pac. J. Math. 175(2), 357-388 (1996)
    • (1996) Pac. J. Math. , vol.175 , Issue.2 , pp. 357-388
    • Bozejko, M.1    Leinert, M.2    Speicher, R.3
  • 9
    • 0000160690 scopus 로고
    • Ψ-independent and symmetrized white noises
    • [BS1]. Accardi, L. (ed.) . World Scientific, Singapore
    • [BS1] Bożejko, M., Speicher, R.: Ψ-independent and symmetrized white noises. In: Accardi, L. (ed.) Quantum Probability and Related Topics VI, 219-236. World Scientific, Singapore, 1991
    • (1991) Quantum Probability and Related Topics , vol.6 , pp. 219-236
    • Bozejko, M.1    Speicher, R.2
  • 10
    • 0002629366 scopus 로고
    • Completely positive maps on Coxeter groups, deformed commutataion relations and operator spaces
    • [BS2]
    • [BS2] Bożejko, M., Speicher, R.: Completely positive maps on Coxeter groups, deformed commutataion relations and operator spaces. Math. Ann. 300, 97-120 (1994)
    • (1994) Math. Ann. , vol.300 , pp. 97-120
    • Bozejko, M.1    Speicher, R.2
  • 11
    • 0009891218 scopus 로고    scopus 로고
    • New examples of convolutions and non-commutative central limit theorems
    • [BW1]
    • [BW1] Bożejko, M., Wysoczański, J.: New examples of convolutions and non-commutative central limit theorems. Banach Cent. Publ. 43, 95-103 (1998)
    • (1998) Banach Cent. Publ. , vol.43 , pp. 95-103
    • Bozejko, M.1    Wysoczański, J.2
  • 12
    • 0035600164 scopus 로고    scopus 로고
    • Remarks on t-transformations of measures and convolutions
    • [BW2]
    • [BW2] Bożejko, M., Wysoczański, J.: Remarks on t-transformations of measures and convolutions. Ann. Inst. Henri Poincare Probab. Stat. 37(6), 737-761 (2001)
    • (2001) Ann. Inst. Henri Poincare Probab. Stat. , vol.37 , Issue.6 , pp. 737-761
    • Bozejko, M.1    Wysoczański, J.2
  • 13
    • 0035607466 scopus 로고    scopus 로고
    • Operator Khinchine inequality in noncommutative probability
    • [B]
    • [B] Buchholz, A.: Operator Khinchine inequality in noncommutative probability. Math. Ann. 319, 1-16 (2001)
    • (2001) Math. Ann. , vol.319 , pp. 1-16
    • Buchholz, A.1
  • 14
    • 0003362637 scopus 로고
    • An introduction to orthogonal polynomials
    • [C]. Gordon and Breach, New York.
    • [C] Chihara, T.S.: An Introduction to Orthogonal Polynomials. Mathematics and its Applications 13. Gordon and Breach, New York. 1978
    • (1978) Mathematics and Its Applications , vol.13
    • Chihara, T.S.1
  • 16
    • 0037631495 scopus 로고    scopus 로고
    • Unification of boolean, monotone, anti-monotone, and tensor independence and Lévy processes
    • [F]
    • [F] Franz, U.: Unification of boolean, monotone, anti-monotone, and tensor independence and Lévy processes. Math. Z. 243, 779-816 (2003)
    • (2003) Math. Z. , vol.243 , pp. 779-816
    • Franz, U.1
  • 17
    • 84973999201 scopus 로고
    • Bounded linear operator between C*-algebras
    • [HaPi]
    • [HaPi] Haagerup, U., Pisier, G.: Bounded linear operator between C*-algebras. Duke Math. J. 71, 889-925 (1993)
    • (1993) Duke Math. J. , vol.71 , pp. 889-925
    • Haagerup, U.1    Pisier, G.2
  • 19
    • 77949569500 scopus 로고    scopus 로고
    • An interacting Fock space with periodic Jacobi parameter obtained from regular graphs in large scale limit
    • [HO]
    • [HO] Hora, A., Obata, N.: An interacting Fock space with periodic Jacobi parameter obtained from regular graphs in large scale limit, to appear in Quantum Information V
    • Quantum Information , vol.5
    • Hora, A.1    Obata, N.2
  • 22
    • 25144486085 scopus 로고    scopus 로고
    • Generalized t-transformatons of probability measures and deformed convolution
    • [KY2]
    • [KY2] Krystek, A.D., Yoshida, H.: Generalized t-transformatons of probability measures and deformed convolution. Probab. Math. Stat. 24(1), 97-119 (2004)
    • (2004) Probab. Math. Stat. , vol.24 , Issue.1 , pp. 97-119
    • Krystek, A.D.1    Yoshida, H.2
  • 23
    • 4544288106 scopus 로고    scopus 로고
    • Cumulants in noncommutative probability theory I
    • [Leh]
    • [Leh] Lehner, F.: Cumulants in noncommutative probability theory I. Math. Z. 248, 67-100 (2004)
    • (2004) Math. Z. , vol.248 , pp. 67-100
    • Lehner, F.1
  • 25
    • 0036447016 scopus 로고    scopus 로고
    • Operator-valued version of conditionally free product
    • [M]
    • [M] Młotkowski, W.: Operator-valued version of conditionally free product. Stud. Math. 153(1), 13-29 (2002)
    • (2002) Stud. Math. , vol.153 , Issue.1 , pp. 13-29
    • Młotkowski, W.1
  • 26
    • 33644982935 scopus 로고    scopus 로고
    • Quantum probabilistic approach to spectral analysis of star graphs
    • [Ob]
    • [Ob] Obata, N.: Quantum Probabilistic Approach to Spectral Analysis of Star Graphs. Interdiscip. Inf. Sci. 10(1), 41-52 (2004)
    • (2004) Interdiscip. Inf. Sci. , vol.10 , Issue.1 , pp. 41-52
    • Obata, N.1
  • 28
    • 18244380955 scopus 로고    scopus 로고
    • The infinite divisibility and orthogonal polynomials with a constant recursion formula in free probability theory
    • [SY]
    • [SY] Saitoh, N., Yoshida, H.: The infinite divisibility and orthogonal polynomials with a constant recursion formula in free probability theory. Probab. Math. Stat. 21(1), 159-170 (2001)
    • (2001) Probab. Math. Stat. , vol.21 , Issue.1 , pp. 159-170
    • Saitoh, N.1    Yoshida, H.2
  • 29
    • 0003217929 scopus 로고
    • Orthogonal polynomials
    • [S], 4th ed., Providence, R. I.
    • [S] Szegö, O.: Orthogonal Polynomials. AMS Colloquium Publications, 23, 4th ed., Providence, R. I. (1975)
    • (1975) AMS Colloquium Publications , vol.23
    • Szegö, O.1
  • 32
    • 33644986958 scopus 로고    scopus 로고
    • Remarks on the s-free convolution
    • [Y1]. Obata, N., Matsui, T., Hora, A. (eds.) Non-commutativity, Infinite Dimensionality and Probability at the Crossroads. . World Scientific, Singapore
    • [Y1] Yoshida, H.: Remarks on the s-free convolution. In: Obata, N., Matsui, T., Hora, A. (eds.) Non-commutativity, Infinite Dimensionality and Probability at the Crossroads. QP-PQ Quantum Probability and White Noise Analysis XVI, 412-433. World Scientific, Singapore (2001)
    • (2001) QP-PQ Quantum Probability and White Noise Analysis , vol.16 , pp. 412-433
    • Yoshida, H.1
  • 33
    • 0344629429 scopus 로고    scopus 로고
    • The weight function on non-crossing partitions for the Δ-convolution
    • [Y2]
    • [Y2] Yoshida, H.: The weight function on non-crossing partitions for the Δ-convolution. Math. Z. 245, 105-121 (2003)
    • (2003) Math. Z. , vol.245 , pp. 105-121
    • Yoshida, H.1


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