Soumyashant Nayak

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Collected Works of Richard V. Kadison


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1950–1959

  • Order properties of bounded self-adjoint operators. Proc. Amer. Math. Soc. 2, (1951). 505–510. (MR0042064)

  • On a conjecture of Murray and von Neumann. (with B. Fuglede). Proc. Nat. Acad. Sci. U. S. A. 37, (1951). 420–425. (MR0043390)

  • On determinants and a property of the trace in finite factors. (with B. Fuglede). Proc. Nat. Acad. Sci. U. S. A. 37, (1951). 425–431. (MR0043391)

  • Isometries of operator algebras. Ann. Of Math. (2) 54, (1951). 325–338. (MR0043392)

  • A representation theory for commutative topological algebra. Mem. Amer. Math. Soc., No. 7 (1951), 39 pp. (MR0044040)

  • Infinite unitary groups. Trans. Amer. Math. Soc. 72, (1952). 386–399. (MR0048455)

  • Some remarks on representations of connected groups. Proc. Nat. Acad. Sci. U. S. A. 38, (1952). 419–423. (MR0048456)

  • A generalized Schwarz inequality and algebraic invariants for operator algebras. Ann. of Math. (2) 56, (1952). 494–503. (MR0051442)

  • Determinant theory in finite factors. (with B. Fuglede). Ann. of Math. (2) 55, (1952). 520–530. (MR0052696)

  • Infinite general linear groups. Trans. Amer. Math. Soc. 76, (1954). 66–91. (MR0060745)

  • The closure of the regular operators in a ring of operators. (with J. Feldman). Proc. Amer. Math. Soc. 5, (1954). 909–916. (MR0068749)

  • The general linear group of infinite factors. Duke Math. J. 22, (1955). 119–122. (MR0067370)

  • On the additivity of the trace in finite factors. Proc. Nat. Acad. Sci. U. S. A. 41, (1955). 385–387. (MR0069402)

  • On the orthogonalization of operator representations. Amer. J. Math. 77 (1955), 600–620. (MR0072442)

  • Isomorphisms of factors of infinite type. Canad. J. Math. 7, 322–327 (1955). (MR*******)

  • Multiplicity theory for operator algebras. Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 169–173. (MR0072443)

  • Report on operator algebras. [TeXed version] Report of an international conference on operator theory and group representations, Arden House, Harriman, N.Y., 1955, pp. 4–10. Publ. 387, National Academy of Sciences-National Research Council, Washington, D.C., 1955. (MR0079731)

  • Operator algebras with a faithful weakly-closed representation. Ann. of Math. (2) 64 (1956), 175–181. (MR0079233)

  • Irreducible Operator Algebras. Proc. Nat. Acad. Sci. U.S.A. 43 (1957), 273--276. (MR*******)

  • Unitary invariants for representations of operator algebras. Ann. of Math. (2) 66 (1957), 304–379. (MR0089378)

  • Three test problems in operator theory. (with I. M. Singer). Pacific J. Math. 7 (1957), 1101–1106. (MR0092123)

  • Theory of operators. II. Operator algebras. Bull. Amer. Math. Soc. 64 1958 61–85. (MR0097298)

  • Extensions of pure states. Amer. J. Math. 81 1959 383–400. (MR0123922)



    • 1960–1969

  • Unitary operators in C*-algebras. (with J. G. Glimm). Pacific J. Math. 10 1960 547–556. (MR0115104)

  • Triangular operator algebras. Fundamentals and hyperreducible theory. (with I. M. Singer). Amer. J. Math. 82 1960 227–259. (MR0121675)

  • The trace in finite operator algebras. Proc. Amer. Math. Soc. 12 1961 973–977. (MR0139961)

  • States and representations. Trans. Amer. Math. Soc. 103 1962 304–319. (MR0139019)

  • Normalcy in operator algebras. Duke Math. J. 29 1962 459–464. (MR0149324)

  • Remarks on the type of von Neumann algebras of local observables in quantum field theory. J. Mathematical Phys. 4 1963 1511–1516. (MR0159585)

  • Transformations of states in operator theory and dynamics. Topology 3 1965 suppl. 2, 177–198. (MR0169073)

  • Derivations of operator algebras. Ann. of Math. (2) 83 1966 280–293. (MR0193527)

  • Automorphisms of operator algebras. (with J. R. Ringrose). Bull. Amer. Math. Soc. 72 1966 1059–1063. (MR0200742)

  • Derivations of operator group algebras. (with J. R. Ringrose). Amer. J. Math. 88 1966 562–576. (MR0203504)

  • Derivations and automorphisms of operator algebras. (with J. R. Ringrose). Comm. Math. Phys. 4 1967 32–63. (MR0206735)

  • The energy momentum spectrum of quantum fields. Comm. Math. Phys. 4 1967 258–260. (MR0213122)

  • Derivations and automorphisms of operator algebras. II. (with E. C. Lawrence and J. R. Ringrose). J. Functional Analysis 1 1967 204–221. (MR0215111)

  • Asymptotically abelian systems. (with S. Doplicher and D. Kastler and D. W. Robinson). Comm. Math. Phys. 6 1967 101–120. (MR0216299)

  • Lectures on operator algebras. 1967 Cargêse Lectures in Theoretical Physics: Application of Mathematics to Problems in Theoretical Physics (Cargêse, 1965) pp. 41–82 Gordon and Breach Science Publ., New York. (MR0229440)

  • Strong continuity of operator functions. Pacific J. Math. 26 1968 121–129. (MR0231211)

  • Pure states and approximate identities. Proc. Amer. Math. Soc. 21 1969 749–752. (MR0240633)



    • 1970–1979

  • Some analytic methods in the theory of operator algebras. 1970 Lectures in Modern Analysis and Applications. II pp. 8–29 Lecture Notes in Mathematics, Vol. 140 Springer, Berlin. (MR0264411)

  • Nets of C*-algebras and classification of states. (with R. Haag and D. Kastler). Comm. Math. Phys. 16 1970 81–104.

  • Equivalence in operator algebras. (With G. K. Pedersen). Math. Scand. 27 (1970), 205–222 (1971). (MR0308803)

  • Cohomology of operator algebras. I. Type I von Neumann algebras. (with J.R. Ringrose). Acta Math. 126 1971 227–243. (MR0283578)

  • Cohomology of operator algebras. II. Extended cobounding and the hyperfinite case. (with J.R. Ringrose). Ark. Mat. 9, 55–63. (1971). (MR0318907)

  • Mappings of operator algebras. Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 2, pp. 389–393. Gauthier-Villars, Paris, 1971. (MR0428066)

  • Perturbations of von Neumann algebras. I. Stability of type. (with D. Kastler). Amer. J. Math. 94 (1972), 38–54. (MR0296713)

  • Cohomology of operator algebras. III. Reduction to normal cohomology. (with J. R. Ringrose and B. E. Johson). Bull. Soc. Math. France 100 (1972), 73–96. (MR0318908)

  • Asymptotic orbits in a free Fermi gas. (with R. Haag and D. Kastler). Comm. Math. Phys. 33 (1973), 1–22. (MR0347295)

  • Algebraic automorphisms of operator algebras. (with J. R. Ringrose). J. London Math. Soc. (2) 8 (1974), 329–334. (MR0348508)

  • A note on derivations of operator algebras. Bull. London Math. Soc. 7 (1975), 41–44. (MR0365162)

  • Book Review - The structure of factors. Bull. Amer. Math. Soc. 81 (1975), no. 3, 522–527. (MR0384004)

  • Automorphisms and quasi-free states of the CAR algebra. (with N. M. Hugelholtz). Comm. Math. Phys. 43 (1975), no. 2, 181–197. (MR0384004)

  • Corrigendum: "Asymptotic orbits in a free Fermi gas" (Comm. Math. Phys. 33 (1973), 1–22). (with R. Haag and D. Kastler). Comm. Math. Phys. 43 (1975), no. 2, 198. (MR0428989)

  • Operator algebras. Algebras in analysis (Proc. Instructional Conf. and NATO Advanced Study Inst., Birmingham, 1973), pp. 101–117. (MR0430796)

  • Notes on the Fermi gas. Symposia Mathematica, Vol. XX (Convegno sulle Algebra C* e loro Applicazioni in Fisica Teorica, Convegno sulla Teoria degli Operatori Indice e Teoria K, INDAM, Rome, 1975), pp. 425–431. Academic Press, London, 1976. (MR0462322)

  • Normal states and unitary equivalence of von Nemann algebras. C*-algebras and their applications to statistical mechanics and quantum field theory (Proc. Internat. School of Physics "Enrico Fermi'', Course LX, Varenna, 1973), pp. 1–18. North-Holland, Amsterdam, 1976. (MR0633778)

  • Similarity of operator algebras. Acta Math. 141 (1978), no. 3-4, 147–163. (MR0491546)

  • Product isometries and automorphisms of the CAR algebra. C*-algebras and applications to physics (Proc. Second Japan-USA Sem., Los Angeles, Calif., 1977), pp. 173–185, Lecture Notes in Math., 650, Springer, Berlin, 1978. (MR0504764)

  • Unbounded similarity. Algèbres d'opérateurs et leurs applications en physique mathématique (Proc. Colloq., Marseille, 1977), pp. 193–199, Colloq. Internat. CNRS, 274, CNRS, Paris, 1979. (MR0560636)



    • 1980–1989

  • Operator algebras – the first forty years. Operator algebras and applications, Part I (Kingston, Ont., 1980), pp. 1–18, Proc. Sympos. Pure Math., 38, Amer. Math. Soc., Providence, R.I., 1982. (MR0679692)

  • Limits of states. Comm. Math. Phys. 85 (1982), no. 1, 143–154. (MR0667773)

  • Diagonalizing matrices over operator algebras. Bull. Amer. Math. Soc. (N.S.) 8 (1983), no. 1, 84–86. (MR0682828)

  • Representations of matricial operator algebras. Operator algebras and group representations, Vol. II (Neptun, 1980), 1–22, Monogr. Stud. Math., 18, Pitman, Boston, MA, 1984. (MR0733299)

  • Diagonalizing matrices. American Journal of Mathematics, 106 (1984), no. 1, 1451–1468. (MR-------)

  • Means and convex combinations of unitary operators. (with G. K. Pedersen). Math. Scand. 57 (1985), no. 2, 249–266. (MR0832356)

  • The von Neumann algebra characterization theorems. Exposition. Math. 3 (1985), no. 3, 193–227.(MR0861016)

  • Algebras of unbounded functions and operators. Exposition. Math. 4 (1986), no. 1, 3–33. (MR0861508)

  • Notes on the canonical anticommutation relations. Statistical mechanics and field theory: mathematical aspects (Groningen, 1985), 281–294, Lecture Notes in Phys., 257, Springer, Berlin, 1986. (MR0862841)

  • The Weyl theorem and block decompositions. Operator algebras and applications, Vol. 1, 109–117, London Math. Soc. Lecture Note Ser., 135, Cambridge Univ. Press, Cambridge, 1988. (MR0996443)

  • Some notes on noncommutative analysis. Analysis at Urbana, Vol. II (Urbana, IL, 1986–1987), 243–257, London Math. Soc. Lecture Note Ser., 138, Cambridge Univ. Press, Cambridge, 1989. (MR1009193)



    • 1990–1999

  • Local derivations. J. Algebra 130 (1990), no. 2, 494–509. (MR1051316)

  • Operator algebras — an overview. The legacy of John von Neumann (Hempstead, NY, 1988), 61–89, Proc. Sympos. Pure Math., 50, Amer. Math. Soc., Providence, RI, 1990. (MR1103388)

  • Reflections relating a von Neumann algebra and its commutant. Mappings of operator algebras (Philadelphia, PA, 1988), 295--304, Progr. Math., 84, Birkhäuser Boston, Boston, MA, 1990. (MR******)

  • Triangular algebras — another chapter. Selfadjoint and nonselfadjoint operator algebras and operator theory (Fort Worth, TX, 1990), 63–76, Contemp. Math., 120, Amer. Math. Soc., Providence, RI, 1991. (MR1126275)

  • A note on the similarity problem. J. Operator Theory 26 (1991), no. 2, 389–405.(MR1225523)

  • On an inequality of Haagerup-Pisier. J. Operator Theory 29 (1993), no. 1, 57–67. (MR1277964)

  • Book Review - Operator algebras in dynamical systems. Bull. Amer. Math. Soc. (N.S.) 28 (1993), no. 1, 133–136.

  • Strategies in the secretary problem. Exposition. Math. 12 (1994), no. 2, 125–144. (MR1274782)

  • Notes on the Gelfand-Neumark theorem. C*-algebras: 1943–1993 (San Antonio, TX, 1993), 20–53, Contemp. Math., 167, Amer. Math. Soc., Providence, RI, 1994. (MR1292008)

  • Affine mappings of invertible operators. (with L. A. Harris). Proc. Amer. Math. Soc. 124 (1996), no. 8, 2415–2422. (MR1340389)

  • Schurian algebras and spectral additivity. (with L. A. Harris). J. Algebra 180 (1996), no. 1, 175–186. (MR1375573)

  • On tensor products for von Neumann algebras. (with L. Ge). Invent. Math. 123 (1996), no. 3, 453–466. (MR1383957)

  • Banach algebras with unitary norms. (with M. L Hansen). Pacific J. Math. 175 (1996), no. 2, 535–552. (MR1432844)

  • On representations of finite type. Proc. Natl. Acad. Sci. USA 95 (1998), no. 23, 13392–13396. (MR1660168)

  • Lajos Pukánszky (1928–1996). (with J. Dixmier and M. Duflo and A. Hajnal and A. Koranyi and J. Rosenberg and M. Vergne). Notices Amer. Math. Soc. 45 (1998), no. 4, 492–499. (MR1614553)

  • Dual cones and Tomita-Takesaki theory. Operator algebras and operator theory (Shanghai, 1997), 151–178, Contemp. Math., 228, Amer. Math. Soc., Providence, RI, 1998. (MR1667660)



    • 2000–2009

  • Which Singer is that? Surveys in differential geometry, 347–373, Surv. Differ. Geom., 7, Int. Press, Somerville, MA, 2000. (MR1919431)

  • On the early work of I. E. Segal. Special issue dedicated to the memory of I. E. Segal. J. Funct. Anal. 190 (2002), no. 1, 15–18. (MR1895525)

  • The Pythagorean theorem. I. The finite case. Proc. Natl. Acad. Sci. USA 99 (2002), no. 7, 4178–4184. (MR1895747)

  • The Pythagorean theorem. II. The infinite discrete case. Proc. Natl. Acad. Sci. USA 99 (2002), no. 8, 5217–5222. (MR1896498)

  • Non-commutative conditional expectations and their applications. Operator algebras, quantization, and noncommutative geometry, 143–179, Contemp. Math., 365, Amer. Math. Soc., Providence, RI, 2004. (MR2106820)

  • Diagonals of self-adjoint operators. (with W. Arveson). Operator theory, operator algebras, and applications, 247–263, Contemp. Math., 414, Amer. Math. Soc., Providence, RI, 2006. (MR2277215)

  • Means of unitary operators, revisited. (with U. Haagerup and G. K. Pedersen). Math. Scand. 100 (2007), no. 2, 193–197. (MR2339367)

  • Irving Kaplansky's role in mid-twentieth century functional analysis. Notices Amer. Math. Soc. 55 (2008), no. 2, 216–225. (MR2375023)

  • A note on projection equivalence in von Neumann algebras. C. R. Math. Acad. Sci. Soc. R. Can. 31 (2009), no. 1, 1–6. (MR2519015)



    • 2010–2019

  • A note on derivations of Murray-von Neumann algebras. (with Z. Liu). Proc. Natl. Acad. Sci. USA 111 (2014), no. 6, 2087–2093. (MR3200173)

  • The Heisenberg relation – mathematical formulations. (with Z. Liu). SIGMA Symmetry Integrability Geom. Methods Appl. 10 (2014), Paper 009, 40 pp. (MR3210626)

  • Derivations of Murray-von Neumann algebras. (with Z. Liu). Math. Scand. 115 (2014), no. 2, 206–228. (MR3291726)

  • A note on commutators in algebras of unbounded operators. (with Z. Liu and A. Thom). Expositiones Mathematicae 38 (2020), no. 2, 232–239.