Frederic W. Shultz
Professor of Mathematics
fshultz [at] wellesley [dot] edu
Department of Mathematics
106 Central Street
Wellesley, MA 02481
Science Center 374B
B.S., California Institute of Technology
Ph.D., University of Wisconsin
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,
- 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
- (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)
- (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)
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
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
- (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
- (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
(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
- Arveson's work on entanglement,
Complex Anal. Oper. Theory (initial electronic version Nov 2013; print version expected fall 2014) (pdf)
(Copyright (2013) Birkhauser. The "electronic first" published article may be found at