Frederic W. Shultz

Professor of Mathematics

Email: fshultz [at] wellesley [dot] edu Address: Department of Mathematics Wellesley College 106 Central Street Wellesley, MA 02481 Office: Science Center 374B Phone: (781)-283-3118 Fax: (781)-283-3642

Education

B.S., California Institute of Technology
Ph.D., University of Wisconsin

Research Interests

My current research involves state spaces of operator algebras and related topics in quantum information theory.

Publications and Preprints

• Axioms for quantum mechanics: a generalized probability theory. Ph. D dissertation, University of Wisconsin, Madison, 1972.
• A characterization of state spaces of orthomodular lattices, Journal of Combinatorial Theory 17 (1974) 317-328.
• (with E. Alfsen): On the geometry of non-commutative spectral theory, Bulletin American Mathematical Society 81 (1975), 893 - 895.
• (with E. Alfsen): Non-commutative spectral theory for affine function spaces on convex sets, Memoirs Amer. Math. Soc. 172, Providence, 1976, 120 pp.
• Events and observables in axiomatic quantum mechanics, International J. of Theoret. Physics 16 (1977) 259-272
• (with E. Alfsen and E. Stormer): A Gelfand-Neumark theorem for Jordan algebras, Advances in Math 28 (1978) 11-56
• (with E. Alfsen): State spaces of Jordan algebras, Acta. Math. 140 (1978) 155-190.
  
• On normed Jordan algebras which are Banach dual spaces, J. Functional Analysis 31 (l979) 360-376.
• (with E. Alfsen and H. Hanche-Olsen) State spaces of C*-algebras, Acta Mathematica 144 (1980), 267-305.
• Dual maps of Jordan homomorphisms and *-homomorphisms between C*-algebras, Pacific. J. Math. 93 (1981), 435-441.
• Pure states as a dual object for C*-algebras, Commun. Math. Physics 82 (1982) 497-509.
• Pure states as a dual object for C*-algebras, Proc. Symp.Pure Math 38 (1982) 413-417 (summary of preceding paper).
• (with B. Iochum) Normal state spaces of Jordan and von Neumann algebras, J. Functional Analysis 50 (1983) 317-328.
• (with C. Akemann) Perfect C*-algebras, Memoirs Amer. Math. Soc. 326, 1985, 117 pg.
  
• (with R. J. Archbold) Characterization of C*-algebras with continuous trace by properties of their pure states, Pacific J. Math 136 (1989) 1-13.
• (with A. Shuchat) The Joy of Mathematica, Addison-Wesley, 1994, Japanese translation 1995, 2nd edition: Harcourt-Brace/Academic Press, 2000.
• (with E. Alfsen) Orientation in operator algebras, Proc. Natl. Acad. Sci. USA 95 (1998) 6596-6601.
• (with E. Alfsen) On Orientation and Dynamics in Operator Algebras, Part I, Commun. Math. Phys. 194 (1998) 87-108.
• (with E. Alfsen) State Spaces of Operator Algebras: Basic Theory, Orientations, and C*-products, Birkhauser Boston, 2001.
• (with E. Alfsen) Geometry of State Spaces of Operator Algebras, Birkhauser Boston, 2003.
• Dimension groups for interval maps, New York Journal of Mathematics 11 (2005) 1-41. (pdf)(NYJM)

The articles below may be downloaded for personal use only. Any other use requires prior permission of the author and the publisher.

• (with V. Deaconu), C*-algebras associated with interval maps, Trans. Amer. Math. Soc. 359 (2007) 1889-1924. (pdf)
• Dimension groups for interval maps: the transitive case. Ergodic Theory and Dynamical Systems, 27 (2007) 1287-1321. (pdf)
• (with E. Alfsen) Unique decompositions, faces, and automorphisms of separable states, J. Math. Phys. 51 (2010) 52201 (pdf) (Copyright (2010) American Institute of Physics. The published article may be found at http://link.aip.org/link/doi/10.1063/1.3399808)
• (with E. Alfsen) Finding decompositions of a class of separable states, Linear Algebra and its Applications 437 (2012) 2613-2629 (pdf) (Copyright (2012) Elsevier Inc. The published article may be found at http://dx.doi.org/10.1016/j.laa.2012.06.018)
• (with V. Paulsen) Complete positivity of the map from a basis to its dual basis, J. Math. Phys. 54 (2013) 072201 (pdf) (Copyright (2013) American Institute of Physics. The published article may be found at http://dx.doi.org/10.1063/1.4812329)
• (with J. Chen, H. Dawkins, Z. Ji, N. Johnston, D. Kribs, B. Zeng) Uniqueness of quantum states compatible with given measurement results. Phys. Rev. A, 88 (2013) 012109. (pdf) (Copyright (2013) American Physical Society. Published article may be found at http://dx.doi.org/10.1103/PhysRevA.88.012109)
• Arveson's work on entanglement, Complex Anal. Oper. Theory (2014) 8: 1507-1512 (pdf) (Copyright (2013) Birkhauser. The published article may be found at may be found at http://dx.doi.org/10.1007/s11785-013-0342-2)
• The structural physical approximation conjecture, J. Math. Phys. 57 (2016), 015218 (pdf) (Copyright (2015) American Institute of Physics. The published article may be found at may be found at http://dx.doi.org/10.1063/1.4938226)