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http://dx.doi.org/10.4134/JKMS.2004.41.1.107

STRUCTURAL PROJECTIONS ON A JBW-TRIPLE AND GL-PROJECTIONS ON ITS PREDUAL  

Hugli, Remo-V. (School of Mathematics Trinity College)
Publication Information
Journal of the Korean Mathematical Society / v.41, no.1, 2004 , pp. 107-130 More about this Journal
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 {$\cdots$} from $A\;\times\;A\;\times\;A\;to\;A$ 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 GL-projections on $A_{*}$. Furthermore, the class of GL-projections on $A_{*}$ is naturally ordered and is completely ortho-additive with respect to L-orthogonality.
Keywords
$JBW^{*}-triple$; structural projection; GL-projection;
Citations & Related Records

Times Cited By Web Of Science : 3  (Related Records In Web of Science)
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연도 인용수 순위
1 Solution of the contractive projection problem /
[ Y.Friedman;B.Russo ] / J. Funct. Anal.   DOI
2 Classification of atomic facially symmetric spaces /
[ Y.Friedman;B.Russo ] / Canad. J. Math.   DOI
3 State Spaces of Jordan algebras /
[ E.M.Alfsen;F.Schultz ] / Acta Math.   DOI
4 Contractive projections on Jordan <TEX>$C^*$</TEX>-algebras and generalisations /
[ W.Kaup ] / Math. Scand.   DOI
5 An application of infinite dimensional holomorphy to the geometry of Banach spaces /
[ J.Arazy ] / Geometrical Aspects of Functional Analysis, Lecture Notes in Math.
6 Peirce inner ideals in <TEX>$Jordan^ *$</TEX>-triples /
[ C.M.Edwards;G.T.Ruttimann ] / J. Algebra   DOI   ScienceOn
7 Orthogonal faces of the unit ball in a Banach space /
[ C.M.Edwards;G.T.Ruttimann ] / Atti Sem. Mat. Fis. Univ. Modena
8 /
[ S.Dineen;J.Mujica(ed.) ] / The second dual of a <TEX>$JB^ *$</TEX>-triple system, Complex Analysis, Functional Analysis and Approximation Theory
9 /
[ C.M.Edwards;R.V.Hugli ] / M-orthogonality and holomorphic rigidity in complex Banach spaces
10 Characterisation of the predual and ideal structure of a <TEX>$JBW^*$</TEX>-triple /
[ G.Horn ] / Math. Scand.
11 Jordan Triple Systems by the Grid Approach /
[ E.Neher ] / Lecture Notes in Math.
12 Uniqueness of Hahn-Banach extensions and unique best approximations /
[ R.R.Phelps ] / Trans. Amer. Math. Soc.   DOI   ScienceOn
13 A Stone-Weierstrass Theorem for <TEX>$JB^*<$</TEX>-Triples /
[ B.Sheppard ] / J. London Math. Soc.   DOI
14 Les automorphismes analytiques isometriques d'un variete complexe normee /
[ J.P.Vigue ] / Bull. Soc. Math. France
15 /
[ H.Hanche-Olsen;E.Stormer ] / Jordan Operator algebras
16 A geometric characterization of structural projections on the predual of aa <TEX>$JBW^ *$</TEX>-triple /
[ C.M.Edwards;R.V.Hugli;G.T.Ruttimann ] / J. Funct. Anal.
17 Complete holomorphic vector fields in the second dual of a Banach space /
[ S.Dineen ] / Math. Scand.   DOI
18 Jordan-Tripelsysteme und die Koecher-Konstruktion von Lie-Algebren /
[ K.Meyberg ] / Math. Z.   DOI
19 Positive projections and Jordan structure in operator algebras /
[ E.G.Effros;E.Stormer ] / Math. Scand.   DOI
20 Inner ideals in quadratic Jordan algebras /
[ K.McCrimmon ] / Trans. Amer. Math. Soc.   DOI   ScienceOn
21 Structural projections on <TEX>$JBW^*$</TEX>-triples /
[ C.M.Edwards;G.T.Ruttimann ] / J. London Math. Soc.   DOI
22 Positivitatsbereiche im <TEX>$\matnbb{R}^m$</TEX> /
[ M.Koecher ] / Amer. J. Math.   DOI   ScienceOn
23 The structure of decoherence functionals for von Neumann quantum histories /
[ J.D.M.Wright ] / J. Math. Phys.   DOI   ScienceOn
24 L-structure in L-spaces /
[ F.Cunningham ] / Trans. Amer. Math. Soc.   DOI   ScienceOn
25 The range of a structural projection /
[ C.M.Edwards;K.McCrimmon;G.T.Ruttimann ] / J. Funct. Anal.   DOI   ScienceOn
26 Bounded Symmetric Domains and JordanPairs /
[ O.Loos ] / Mathematical Lectures
27 Structure of <TEX>$JB^*<$</TEX>-triples /
[ B.Russo;W.Kaup(ed.);McCrimmon(ed.);H.Petersson(ed.) ] / Jordan Algebras, Proceedings of the Conference held in Oberwolfach
28 A projection principle concerning biholomorphic automorphisms /
[ L.L.Stacho ] / Acta. Sci. Math.
29 Injectivity and operator spaces /
[ M.D.Choi;E.G.Effros ] / J. Funct. Anal.   DOI
30 Compatible subtriples of <TEX>$Jordan^ *$</TEX>-triples /
[ C.M.Edwards;D.Lorch;G.T.Ruttimann ] / J. Algebra   DOI   ScienceOn
31 Gleason's Theorem for rectangular <TEX>$JBW^*$</TEX>-triples /
[ C.M.Edwards;G.T.Ruttimann ] / Commun. Math. Phys.   DOI   ScienceOn
32 Holomorphic characterization of Jourdan <TEX>$C^ *$</TEX>-algebras /
[ R.Braun;W.Kaup;H.Upmeier ] / Math. Z.   DOI
33 A generalisation of <TEX>$C^*$</TEX>-algebras /
[ L.A.Harris ] / Proc. London Math. Soc.   DOI
34 Linear algebraic groups in infinite dimensions /
[ L.A.Harris;W.Kaup ] / IIIinios J. Math.
35 Jordan algebras in analysis, operator theory and quantum mechanics /
[ H.Upmeier ] / Providence Amer. Math. Soc.
36 Espaces L-facteurs biduaux: bonne disposition, meilleure approximation et propriete de Radon-Nikodym /
[ D.Li ] / Quart. J. Math. Oxford   DOI
37 /
[ C.M.Edwards;R.V.Hugli ] / Order structure of GL-projections on the predual of a <TEX>$JBW^ *$</TEX>-triple
38 Jordan structures in analysis /
[ A. Rodriguez Palacios;W.Kaup(ed.);K.McCrimmon(ed.);H.Petersson(ed.) ] / Jordan Algebras, Proceedings of the Conference held in Oberwolfach
39 Le groupe des automorphismes analytiques d'un domaine borne d'un espace de Banach complexe /
[ J.P.Vigue ] / Ann. Sci. Ecole Norm. Sup.   DOI
40 /
[ E.M.Alfsen;F.Schultz ] / State Spaces of Operator Algebras
41 The lattice of <TEX>$weak^*$</TEX>-closed inner ideals in a <TEX>$W^*$</TEX>-algebra /
[ C.M.Edwards;G.T.Ruttimann ] / Commun. Math. Phys.   DOI   ScienceOn
42 Sur les domaines bornes homogenes de l'espace de n variables complexes /
[ E.Cartan ] / Abh. Math. Sem. Univ. Hamburg   DOI
43 Conditional expectation and bicontractive projections on Jordan <TEX>$C^*$</TEX>-algebras and their generalisations /
[ Y.Friedman;B.Russo ] / Math. Z.   DOI
44 M-structure in dual Banach spaces /
[ F.Cunningham;E.G.Effros;N.Roy ] / Israel J. Math.   DOI
45 Complex measures on projections in von Neumann algebras /
[ L.J.Bunce;J.D.M.Wright ] / J. London Math. Soc.   DOI
46 Inner ideals in the bi-Cayley triple /
[ C.M.Edwards;G.T.Ruttimann ] / Atti Sem. Mat. Fis. Univ. Modena
47 A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces /
[ W.Kaup ] / Math. Z.   DOI
48 /
[ M.Neal;B.Russo ] / State Spaces on <TEX>$JB^*$</TEX>-Triples
49 Les domaines bornes symetriques d'un espace de Banach et les systemes triples de Jordan /
[ J.P.Vigue ] / Math. Ann.   DOI
50 The Mackey-Gleason problem for vector measures on projections in von Neumann algebras /
[ L.J.Bunce;J.D.M.Wright ] / J. London Math. Soc.   DOI
51 Cones autopolaires et algebres de Jordan /
[ B.Iochum ] / Lecture Notes in Mathe.
52 Bounded symmetric domains in infinite dimensional spaces /
[ L.A.Harris;T.L.Hayden(ed.);T.J.Suffridge ] / Proceedings on Infinite Dimensional Holomorphy, Lecture Notes in Math   DOI
53 <TEX>$Weak^ *$</TEX>-continuity of Jordan triple products and its applications /
[ T.J.Barton;R.M.Timoney ] / Math. Scand.   DOI
54 Structure of the predual of a <TEX>$JBW^*$</TEX>-triple /
[ Y.Friedman;B.Russo ] / J. Reine Angew. Math.
55 Inner ideals in exceptional <TEX>$JBW^*$</TEX>-triples /
[ C.M.Edwards;G.T.Ruttimann;S.Vasilovsky ] / Michigan Math. J.   DOI