본문 바로가기
KERD
논문KCI 등재

Structural projections on a JBW$^*$-triple and GL-projectionson its Predual

Remo V. H\
대한수학회 (The Korean Mathematical Society)|2004.01|대한수학회지 (Journal of the KMS)|제41권 제1호|pp. 107-130

0

조회

0

다운로드

0

인용

0

참고문헌

주제분류수학

초록

Abstract

A JB∗-triple is a Banach space A on which the group Aut(B) of biholomorphic automorphisms acts transitively on the open unit ball B of A. In this case, a triple product {· · · } from A × A × A to A can be defined in a canonical way. If A is also the dual of some Banach space A∗, then A is said to be a JBW∗- triple. A projection R on A is said to be structural if the identity {Ra, b, Rc} = R{a, Rb, c, } holds. On JBW∗-triples, structural projections being algebraic objects by definition have also some interesting metric properties, and it is possible to give a full characterization of structural projections in terms of the norm of the predual A∗ of A. It is shown, that the class of structural projections on A coincides with the class of the adjoints of neutral GLprojections on A∗. Furthermore, the class of GL-projections on A∗ is naturally ordered and is completely ortho-additive with respect to L-orthogonality.

참고문헌 (45)

  1. "State Spaces of Jordan algebras" (1978)
  2. "State Spaces of Operator Algebras" (2001)
  3. "An application of innite dimensional holomorphy to the geometry ofBanach spaces Geometrical Aspects of Functional Analysis" (1980)
  4. "Weak-continuity of Jordan triple products andits applications" (1986)
  5. "Holomorphic characterization of JordanC-algebras" (1987)
  6. "Complex measures on projections in von Neu-mann algebras" (1992)
  7. "The Mackey-Gleason problem for vector measureson projections in von Neumann algebras" (1994)
  8. "L-structure in L-spaces" (1960)
  9. "M-structure in dual Banach spaces" (1973)
  10. "Complete holomorphic vector elds in the second dual of a Banachspace" (1986)
  11. "The second dual of a JB-triple system", pp.6769~ (1986), North-Holland
  12. "A geometric characterizationof structural projections on the predual of a JBW-triple to appear in J. Funct.Anal."
  13. "Order structure of GL-projections on the predual of a JBW-triple"
  14. "Compatible subtriples ofJordan-triples", 216, pp.707~740 (1999)
  15. "The range of a structuralprojection", 139, pp.196~224 (1996)
  16. "Structural projections on JBW-triples", 53, pp.354~368 (1996)
  17. "Peirce inner ideals in Jordan-triples", 180, pp.4166~ (1996)
  18. "The lattice of weak-closed inner ideals in a W-algebra", 197, pp.131~166 (1998)
  19. "Gleasons Theorem for rectangular JBW-triples", 203, pp.269~295 (1999)
  20. "Inner ideals in the bi-Cayley triple", pp.235~259 (1999), Atti Sem. Mat. Fis. Univ.
  21. "Orthogonal faces of the unit bal in a Banach space", 49, pp.473~493 (2001), Atti Sem. Mat. Fis.Univ.
  22. "Inner ideals in exceptionalJBW-triples" (1993)
  23. "Positive projections and Jordan structure in operatoralgebras" (1979)
  24. "Structure of the predual of a JBW-triple", pp.6789~ (1985)
  25. "Solution of the contractive projection problem", pp.5679~ (1985)
  26. "Conditional expectation and bicontractive projections on JordanC-algebras and their generalisations" (1987)
  27. "Classication of atomic facially symmetric spaces", pp.3387~ (1993)
  28. "A generalisation of C-algebras" (1981)
  29. "Bounded symmetric domains in innite dimensional spaces. Proceedings on Innite Dimensional Holo-morphy Lecture Notes in Math.364", pp.13~40 (1974)
  30. "Linear algebraic groups in innite dimensions" (1977)
  31. "Characterisation of the predual and ideal structure of a JBW-triple" (1983)
  32. "Lecture Notes in Mathe.1049" (1984)
  33. "A Riemann mapping theorem for bounded symmetric domains in com-plex Banach spaces" (1983)
  34. "Contractive projections on Jordan C-algebras and generalisations", pp.95100~ (1984)
  35. O. Loos, "University of California" (1977)
  36. K. McCrimmon, "Inner ideals in quadratic Jordan algebras" (1971)
  37. K. Meyberg, "Jordan-Tripelsysteme und die Koecher-Konstruktion von Lie-Algebren", pp.5878~ (1970)
  38. M. Neal, "State Spaces on JB-Triples"
  39. E. Neher, "Jordan Triple Systems by the Grid Approach Lecture Notes in Math.1280" (1987)
  40. R. Phelps, "Uniqueness of Hahn-Banach extensions and unique best approxi-mations" (1960)
  41. "Jordan structures in analysis Proceedings of the Conferenceheld in Oberwolfach" (1994)
  42. "Structure of JB-triples Proceedings of the Conference held in Oberwolfach" (1994)
  43. "A Stone-Weierstrass Theorem for JB-Triples", 65(2), pp.381~396 (2002)
  44. "Jordan algebras in analysis" (1986)
  45. J. D. M. Wright, "The structure of decoherence functionals for von Neumannquantum histories", 36, pp.5409~5413 (1995)

관련 논문AI추천

Second preduals of tridual von Neumann algebras are geometrically uniqueA. I. Shtern장전수학회 · Advanced Studies in Contemporary Mathematics2008 · 제17권 제1호Q-measures on the dual unit ball of a JB${}^*$-tripleC. Martin Edwards, Lina Oliveira대한수학회 · 대한수학회지2019 · 제56권 제1호Jordan (φ, ψ)-derivations in JB^*-triplesAbbas Najati, Mohammad Sal Moslehian대한수학회 · 대한수학회논문집2011 · 제26권 제4호Some remarks on $M$-ideals and strong proximinalityCatherine Finet, Lucas Quarta대한수학회 · 대한수학회보2003 · 제40권 제3호A note on invariant subspaces for operator algebrasAlan Lambert대한수학회 · 대한수학회보2003 · 제40권 제4호Maps preserving Jordan and $\ast$-Jordan triple product on operator $\ast$-algebrasAli Taghavi, Mehran Razeghi, Mojtaba Nouri, Vahid Darvish대한수학회 · 대한수학회보2019 · 제56권 제2호

이 간행물의 다른 논문 (14건)

Composition operators on uniform algebras and the pseudohyperbolic metricT. W. Gamelin, P. Galindo, M. Lindstr\pp. 1-20Functions attaining the supremum and isomorphic properties of a Banach spaceManuel Ruiz, Julio Becerra Guerrero, Mar\'{\i}a D. Acostapp. 21-38Holomorphic functions and the BB-property on product spacesChristopher Boydpp. 39-50Properties of Q-reflexive locally convex spacesMilena Venkovapp. 51-64On universal functionsDinesh Markose, Richard Aronpp. 65-76
원문 보기