Soumyashant Nayak

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Collected Works of William B. Arveson


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1960–1969

  • Prediction Theory and Group Representations. ProQuest LLC, Ann Arbor, MI, 1964, 69 pp. (MR2614448)

  • A theorem on the action of abelian unitary groups. Pacific J. Math. 16 (1966), 205–212. (MR0188809)

  • An algebraic conjugacy invariant for measure preserving transformations. Bull. Amer. Math. Soc. 73 (1967), 121–125. (MR0202970)

  • Operator algebras and measure preserving automorphisms. Acta Math. 118 (1967), 95–109. (MR0210866)

  • A density theorem for operator algebras. Duke Math. J. 34 (1967), 635–647. (MR0221293)

  • Analyticity in operator algebras. Amer. J. Math. 89 (1967), 578–642. (MR0223899)

  • A note on invariant subspaces. (with J. Feldman). Michigan Math. J. 15 (1968), 61–64. (MR0223922)

  • On subalgebras of C*-algebras. Bull. Amer. Math. Soc. 75 (1969), 790–794. (MR0247483)

  • Operator algebras and measure preserving automorphisms. II. (with K. B. Josephson). J. Functional Analysis 4 (1969), 100–134. (MR0250081)

  • Subalgebras of C*-algebras. Acta Math. 123 (1969), 141–224. (MR0253059)



    • 1970–1979

  • Unitary invariants for compact operators. Bull. Amer. Math. Soc. 76 (1970), 88–91. (MR0251576)

  • Operators with compact imaginary part. Indiana Univ. Math. J. 20 (1971), no. 10, 877–878. (MR0410467)

  • Lattices of invariant subspaces. Bull. Amer. Math. Soc. 78 (1972), 515–519. (MR0298451)

  • Subalgebras of C*-algebras. II. Acta Math. 128 (1972), no. 3-4, 271–308. (MR0394232)

  • On groups of automorphisms of operator algebras. J. Functional Analysis 15 (1974), 217–243. (MR0348518)

  • Operator algebras and invariant subspaces. Ann. of Math. (2) 100 (1974), 433–532. (MR0365167)

  • A note on essentially normal operators. Proc. Roy. Irish Acad. Sect. A 74 (1974), 143–146. (MR0365217)

  • Interpolation problems in nest algebras. J. Functional Analysis 20 (1975), no. 3, 208–233. (MR0383098)

  • A spectral theorem for nonlinear operators. Bull. Amer. Math. Soc. 82 (1976), no. 3, 511–513. (MR0417882)

  • Notes on extensions of C*-algebras. Duke Math. J. 44 (1977), no. 2, 329–355. (MR0438137)

  • Perturbations of nest algebras. (with T. Fall and P. Muhly). J. Operator Theory 1 (1979), no. 1, 137–150. (MR0526295)



    • 1980–1989

  • The harmonic analysis of automorphism groups. Proc. Sympos. Pure Math., 38, American Mathematical Society, Providence, RI, 1982, pp. 199–269. (MR0679706)

  • Quantization and the uniqueness of invariant structures. Comm. Math. Phys. 89 (1983), no. 1, 77–102. (MR0707773)

  • Perturbation theory for groups and lattices. J. Funct. Anal. 53 (1983), no. 1, 22–73. (MR0715546)

  • Addendum: ``Quantization and the uniqueness of invariant structures''. Comm. Math. Phys. 93 (1984), no. 1, 141. (MR0737466)

  • Circular operators. Indiana Univ. Math. J. 33 (1984), no. 4, 583–595. (MR0749316)

  • Ten lectures on operator algebras. CBMS Regional Conf. Ser. in Math., 55, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1984, viii+93 pp. (MR0762819)

  • Continuous nests and the absorption principle. Lecture Notes in Math., 1132, Springer-Verlag, Berlin, 1985, 17–29. (MR0799560)

  • Markov operators and OS-positive processes. J. Funct. Anal. 66 (1986), no. 2, 173–234. (MR0832989)

  • Nonlinear states on C*-algebras. Contemp. Math., 62, American Mathematical Society, Providence, RI, 1987, 283–343. (MR0878385)

  • An addition formula for the index of semigroups of endomorphisms of B(H). Pacific J. Math. 137 (1989), no. 1, 19–36. (MR0983326)

  • Continuous analogues of Fock space. Mem. Amer. Math. Soc. 80 (1989), no. 409, iv+66 pp. (MR0987590)

  • Continuous analogues of Fock space. III. Singular states. J. Operator Theory 22 (1989), no. 1, 165–205. (MR1026080)



    • 1990–1999

  • Continuous analogues of Fock space. II. The spectral C*-algebra. J. Funct. Anal. 90 (1990), no. 1, 138–205. (MR1047579)

  • Continuous analogues of Fock space. IV. Essential states. Acta Math. 164 (1990), no. 3–4, 265–300. (MR1049159)

  • Quantizing the Fredholm index (M). Pitman Res. Notes Math. Ser., 225, Longman Scientific & Technical, Harlow; copublished in the United States with, 1990, 1–31. (MR1075632)

  • The spectral C*-algebra of an E0-semigroup. Proc. Sympos. Pure Math., 51, Part 1, American Mathematical Society, Providence, RI, 1990, 1–15. (MR1077377)

  • C*-algebras associated with sets of semigroups of isometries. Internat. J. Math. 2 (1991), no. 3, 235–255. (MR1104118)

  • Discretized CCR algebras. J. Operator Theory 26 (1991), no. 2, 225–239. (MR1225515)

  • A note on extensions of semigroups of *-endomorphisms. (with A. Kishimoto). Proc. Amer. Math. Soc. 116 (1992), no. 3, 769–774. (MR1098393)

  • Improper filtrations for C*-algebras: spectra of unilateral tridiagonal operators (M). Acta Sci. Math. (Szeged) 57 (1993), no. 1–4, 11–24. (MR1243265)

  • Noncommutative spheres and numerical quantum mechanics (M). Res. Notes Math., 5, A K Peters, Ltd., Wellesley, MA, 1993, 1–10. (MR1259055)

  • C*-algebras and numerical linear algebra. J. Funct. Anal. 122 (1994), no. 2, 333–360. (MR1276162)

  • The role of C*-algebras in infinite-dimensional numerical linear algebra. Contemp. Math., 167, American Mathematical Society, Providence, RI, 1994, 114–129. (MR1292012)

  • E0-semigroups in quantum field theory. Proc. Sympos. Pure Math., 59, American Mathematical Society, Providence, RI, 1996, 1–26. (MR1392982)

  • Minimal E0-semigroups (M). Fields Inst. Commun., 13, American Mathematical Society, Providence, RI, 1997, 1–12. (MR1424953)

  • The index of a quantum dynamical semigroup. J. Funct. Anal. 146 (1997), no. 2, 557–588. (MR1452003)

  • Path spaces, continuous tensor products, and E0-semigroups. NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., 495, Kluwer Academic Publishers Group, Dordrecht, 1997, 1–111. (MR1452003)

  • Pure E0-semigroups and absorbing states. Comm. Math. Phys. 187 (1997), no. 1, 19–43. (MR1463821)

  • Dynamical invariants for noncommutative flows (M). International Press, Cambridge, MA, 1997, 476–514. (MR1491137)

  • Subalgebras of C*-algebras. III. Multivariable operator theory. Acta Math. 181 (1998), no. 2, 159–228. (MR1668582)

  • The curvature of a Hilbert module over C[z1,…,zd]. Proc. Natl. Acad. Sci. USA 96 (1999), no. 20, 11096–11099. (MR1712636)

  • On the index and dilations of completely positive semigroups. Internat. J. Math. 10 (1999), no. 7, 791–823. (MR1728123)



    • 2000–2009

  • Interactions in noncommutative dynamics. Comm. Math. Phys. 211 (2000), no. 1, 63–83. (MR1757006)

  • The curvature invariant of a Hilbert module over C[z1,…,zd] (RW) . J. Reine Angew. Math. 522 (2000), 173–236. (MR1758582)

  • Infinite tensor products of completely positive semigroups. (with G. Price). J. Evol. Equ. 1 (2001), no. 2, 221–242. (MR1846747)

  • The heat flow of the CCR algebra (RW). Bull. London Math. Soc. 34 (2002), no. 1, 73–83. (MR1866430)

  • The Dirac operator of a commuting d-tuple (RW). J. Funct. Anal. 189 (2002), no. 1, 53–79. (MR1887629)

  • The domain algebra of a CP-semigroup (RW). Pacific J. Math. 203 (2002), no. 1, 67–77. (MR1895925)

  • Generators of non-commutative dynamics. Ergodic Theory Dynam. Systems 22 (2002), no. 4, 1017–1030. (MR1925633)

  • The structure of spin systems. (with G. Price). Internat. J. Math. 14 (2003), no. 2, 119–137. (MR1966768)

  • Noncommutative dynamics and E-semigroups (BK). Springer Monogr. Math. Springer-Verlag, New York, 2003, x+434 pp. (MR1978577)

  • Four lectures on noncommutative dynamics. Contemp. Math., 335 American Mathematical Society, Providence, RI, 2003, 1–55. (MR2026010)

  • The free cover of a row contraction. Doc. Math. 9 (2004), 137–161. (MR2054985)

  • Asymptotic stability. I. Completely positive maps. Internat. J. Math. 15 (2004), no. 3, 289–312. (MR2060791)

  • The universal A-dynamical system. Contemp. Math., 365 American Mathematical Society, Providence, RI, 2004, 27–39. (MR2106815)

  • p-summable commutators in dimension d. J. Operator Theory 54 (2005), no. 1, 101–117. (MR2168861)

  • On the existence of E0-semigroups (RW). Infin. Dimens. Anal. Quantum Probab. Relat. Top. 9 (2006), no. 2, 315–320. (MR2235552)

  • Diagonals of self-adjoint operators. Contemp. Math., 414 American Mathematical Society, Providence, RI, 2006, 247–263. (MR2277215)

  • Diagonals of normal operators with finite spectrum. Proc. Natl. Acad. Sci. USA 104 (2007), no. 4, 1152–1158. (MR2303566)

  • The asymptotic lift of a completely positive map. J. Funct. Anal. 248 (2007), no. 1, 202–224. (MR2329688)

  • Quotients of standard Hilbert modules. Trans. Amer. Math. Soc. 359 (2007), no. 12, 6027–6055. (MR2329688)

  • Asymptotic lifts of positive linear maps. (with E. Stormer). Pacific J. Math. 233 (2007), no. 1, 1–14. (MR2366366)

  • Lifting endomorphisms to automorphisms. (with D. Courtney). Proc. Amer. Math. Soc. 136 (2008), no. 6, 2073–2079. (MR2383513)

  • The noncommutative Choquet boundary. J. Amer. Math. Soc. 21 (2008), no. 4, 1065–1084. (MR2425180)

  • The probability of entanglement. Comm. Math. Phys. 286 (2009), no. 1, 283–312. (MR2470932)

  • Quantum channels that preserve entanglement. Math. Ann. 343 (2009), no. 4, 757–771. (MR2471599)

  • Maximal vectors in Hilbert space and quantum entanglement. J. Funct. Anal. 256 (2009), no. 5, 1476–1510. (MR2490227)



    • 2010–2012

  • The noncommutative Choquet boundary III: operator systems in matrix algebras. Math. Scand. 106 (2010), no. 2, 196–210. (MR2641960)

  • Dilation theory yesterday and today. Oper. Theory Adv. Appl., 207 Birkhäuser Verlag, Basel, 2010, 99–123. (MR2743416)

  • The noncommutative Choquet boundary II: hyperrigidity. Israel J. Math. 184 (2011), 349–385. (MR2823981)