참고문헌
- C. A. Akemann, The general Stone-Weierstrass problem, J. Functional Analysis 4 (1969), 277-294. https://doi.org/10.1016/0022-1236(69)90015-9
- C. A. Akemann and S. Eilers, Regularity of projections revisited, J. Operator Theory 48 (2002), no. 3, suppl., 515-534.
- E. M. Alfsen, Compact Convex Sets and Boundary Integrals, Springer-Verlag, New York, 1971.
- E. M. Alfsen and F. W. Shultz, State spaces of Jordan algebras, Acta Math. 140 (1978), no. 3-4, 155-190. https://doi.org/10.1007/BF02392307
- E. M. Alfsen, F. W. Shultz, and E. Strmer, A Gelfand-Naimark theorem for Jordan algebras, Adv. Math. 28 (1978), 11-56. https://doi.org/10.1016/0001-8708(78)90044-0
- L. Asimow and A. J. Ellis, Convexity Theory and its Applications in Functional Analysis, London Mathematical Society Monographs, 16, Academic Press, Inc., London, 1980.
- T. J. Barton, T. Dang, and G. Horn, Normal representations of Banach Jordan triple systems, Proc. Amer. Math. Soc. 102 (1988), no. 3, 551-555. https://doi.org/10.1090/S0002-9939-1988-0928978-2
- T. J. Barton and R. M. Timoney, Weak*-continuity of Jordan triple products and its applications, Math. Scand. 59 (1986), no. 2, 177-191. https://doi.org/10.7146/math.scand.a-12160
- M. Battaglia, Order theoretic type decomposition of JBW*-triples, Quart. J. Math. Oxford Ser. (2) 42 (1991), no. 166, 129-147. https://doi.org/10.1093/qmath/42.1.129
- F. F. Bonsall and J. Duncan, Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras, London Mathematical Society Lecture Note Series, 2, Cambridge University Press, London, 1971.
- H. G. Dales, A. T-M. Lau, and D. Strauss, Second duals of measure algebras, Dissertationes Mathematicae (Rozprawy Matematyczne) 481 (2012), 1-121. https://doi.org/10.4064/dm481-0-1
- S. Dineen, Complete holomorphic vector fields on the second dual of a Banach space, Math. Scand. 59 (1986), no. 1, 131-142. https://doi.org/10.7146/math.scand.a-12158
- S. Dineen, The second dual of a JB* triple system, in Complex analysis, functional analysis and approximation theory (Campinas, 1984), 67-69, North-Holland Math. Stud., 125, Notas Mat., 110, North-Holland, Amsterdam, 1986.
- C. M. Edwards, On Jordan W*-algebras, Bull. Sci. Math. (2) 104 (1980), no. 4, 393-403.
- C. M. Edwards, F. J. Fernandez-Polo, C. S. Hoskin, and A. M. Peralta, On the facial structure of the unit ball in a JB*-triple, J. Reine Angew. Math. 641 (2010), 123-144.
- C. M. Edwards and R. V. Hugli, Decoherence in pre-symmetric spaces, Rev. Mat. Complut. 21 (2008), no. 1, 219-249.
- C. M. Edwards, R. V. Hugli, and G. T. Ruttimann, A geometric characterization of structural projections on a JBW*-triple, J. Funct. Anal. 202 (2003), no. 1, 174-194. https://doi.org/10.1016/S0022-1236(02)00064-2
- C. M. Edwards and L. Oliveira, Local facial structure and norm-exposed faces of the unit ball in a JB*-triple, J. Math. Anal. Appl. 421 (2015), no. 2, 1315-1333. https://doi.org/10.1016/j.jmaa.2014.07.073
- C. M. Edwards and G. T. Ruttimann, On the facial structure of the unit balls in a GL-space and its dual, Math. Proc. Cambridge Philos. Soc. 98 (1985), no. 2, 305-322. https://doi.org/10.1017/S0305004100063489
- C. M. Edwards and G. T. Ruttimann, On the facial structure of the unit ball of a GM-space, Math. Z. 193 (1986), no. 4, 597-611. https://doi.org/10.1007/BF01160478
- C. M. Edwards and G. T. Ruttimann, On the facial structure of the unit balls in a JBW*-triple and its predual, J. London Math. Soc. (2) 38 (1988), no. 2, 317-332. https://doi.org/10.1112/jlms/s2-38.2.317
- C. M. Edwards and G. T. Ruttimann, Compact tripotents in bi-dual JB*-triples, Math. Proc. Cambridge Philos. Soc. 120 (1996), no. 1, 155-173. https://doi.org/10.1017/S0305004100074740
- C. M. Edwards and G. T. Ruttimann, The lattice of compact tripotents in bi-dual JB*-triples, Atti Sem. Mat. Fis. Univ. Modena 45 (1997), no. 1, 155-168.
- C. M. Edwards and G. T. Ruttimann, Exposed faces of the unit ball in a JBW*-triple, Math. Scand. 82 (1998), no. 2, 287-304. https://doi.org/10.7146/math.scand.a-13838
- C. M. Edwards and G. T. Ruttimann, Orthogonal faces of the unit ball in a Banach space, Atti Sem. Mat. Fis. Univ. Modena 49 (2001), no. 2, 473-493.
- E. G. Effros, Order ideals in a C*-algebra and its dual, Duke Math. J. 30 (1963), 391-411. https://doi.org/10.1215/S0012-7094-63-03042-4
- F. J. Fernandez-Polo and A. M. Peralta, Compact tripotents and the Stone-Weierstrass theorem for C*-algebras and JB*-triples, J. Operator Theory 58 (2007), no. 1, 157-173.
- F. J. Fernandez-Polo and A. M. Peralta, Non-commutative generalisations of Urysohn's lemma and hereditary inner ideals, J. Funct. Anal. 259 (2010), no. 2, 343-358. https://doi.org/10.1016/j.jfa.2010.04.003
- F. J. Fernandez-Polo and A. M. Peralta, On the facial structure of the unit ball in the dual space of a JB*-triple, Math. Ann. 348 (2010), no. 4, 1019-1032. https://doi.org/10.1007/s00208-010-0511-9
- Y. Friedman, Bounded symmetric domains and the JB*-triple structure in physics, in Jordan algebras (Oberwolfach, 1992), 61-82, de Gruyter, Berlin, 1994.
- Y. Friedman, Physical Applications of Homogeneous Balls, Progress in Mathematical Physics, 40, Birkhauser Boston, Inc., Boston, MA, 2005.
- Y. Friedman and Y. Gofman, Why does the geometric product simplify the equations of physics?, Internat. J. Theoret. Phys. 41 (2002), no. 10, 1841-1855. https://doi.org/10.1023/A:1021048722241
- Y. Friedman and Y. Gofman, Relativistic linear spacetime transformations based on symmetry, Found. Phys. 32 (2002), no. 11, 1717-1736. https://doi.org/10.1023/A:1021450706566
- Y. Friedman and B. Russo, Structure of the predual of a JBW*-triple, J. Reine Angew. Math. 356 (1985), 67-89.
- H. Hanche-Olsen and E. Strmer, Jordan Operator Algebras, Monographs and Studies in Mathematics, 21, Pitman (Advanced Publishing Program), Boston, MA, 1984.
- D. J. Hebert and H. E. Lacey, On supports of regular Borel measures, Pacific J. Math. 27 (1968), 101-118. https://doi.org/10.2140/pjm.1968.27.101
- G. Horn, Characterization of the predual and ideal structure of a JBW*-triple, Math. Scand. 61 (1987), no. 1, 117-133. https://doi.org/10.7146/math.scand.a-12194
- N. Jacobson, Structure and Representations of Jordan Algebras, Amer. Math. Soc. Publications 39, Providence, Rhode Island, 1968.
- W. Kaup, A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces, Math. Z. 183 (1983), no. 4, 503-529. https://doi.org/10.1007/BF01173928
- W. Kaup, Contractive projections on Jordan C*-algebras and generalizations, Math. Scand. 54 (1984), no. 1, 95-100. https://doi.org/10.7146/math.scand.a-12043
- O. Loos, Jordan pairs, Lecture Notes in Mathematics, Vol. 460, Springer-Verlag, Berlin, 1975.
- K. McCrimmon, A Taste of Jordan Algebras, Universitext, Springer-Verlag, New York, 2004.
- M. Neal, Inner ideals and facial structure of the quasi-state space of a JB-algebra, J. Funct. Anal. 173 (2000), no. 2, 284-307. https://doi.org/10.1006/jfan.2000.3577
- E. Neher, Jordan Triple Systems by the Grid Approach, Lecture Notes in Mathematics 1280, Springer-Verlag, Berlin, 1987.
- G. K. Pedersen, C*-Algebras and their Automorphism Groups, London Mathematical Society Monographs 14, Academic Press, London, 1979.
- S. Sakai, C*-Algebras and W*-Algebras, Springer, Berlin,1971.
- F. W. Shultz, On normed Jordan algebras which are Banach dual spaces, J. Funct. Anal. 31 (1979), no. 3, 360-376. https://doi.org/10.1016/0022-1236(79)90010-7
- M. Takesaki, Faithful states of a C*-algebra, Pacific J. Math. 52 (1974), 605-610. https://doi.org/10.2140/pjm.1974.52.605
- M. Tomita, Spectral theory of operator algebras. I, Math. J. Okayama Univ. 9 (1959/1960), 63-98.
- H. Upmeier, Symmetric Banach manifolds and Jordan C*-algebras, North-Holland Mathematics Studies, 104, North-Holland Publishing Co., Amsterdam, 1985.
- H. Upmeier, Jordan Algebras in Analysis, Operator Theory, and Quantum Mechanics, CBMS Regional Conference Series in Mathematics, 67, Published for the Conference Board of the Mathematical Sciences, Washington, DC, 1987.
- J. D. M. Wright, Jordan C*-algebras, Michigan Math. J. 24 (1977), no. 3, 291-302. https://doi.org/10.1307/mmj/1029001946
- M. A. Youngson, A Vidav theorem for Banach Jordan algebras, Math. Proc. Cambridge Philos. Soc. 84 (1978), no. 2, 263-272. https://doi.org/10.1017/S0305004100055092