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Hasse-Schmidt Derivations on Banach-Jordan Pairs

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Abstract (2. Language): 
The aim of this paper consists in establishing the automatic continuity of Hasse-Schmidt derivations on Banach-Jordan Pairs and Banach-Jordan Algebras satisfying some algebraic conditions. Namely, higher derivations on semiprimitive Banach-Jordan Pairs and semiprimitive Banach-Jordan Algebras are continuous.
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REFERENCES

References: 

[I] J. Anquela and T. Cortes, Primitive Jordan Pairs and triple systems, J. Algebra 184 (1996), 632-678.
[2] J. Anquela and T. Cortes, Primitivity in Jordan systems is Uhiquitous, J. Algebra
202 (1998), 295-314.
[3] J. Anquela, T. Cortes, and F. Montaner, On primitive Jordan algehras, J. Algebra
163 (1998), 663-674.
[4] T. J. Barton and Y. Friedman, Bounded derivations on JB*—triples, Quart. J.
Math. 41 (1990), 255-268.
[5] P.E. Bland, Higher derivations on rings and modules, Int. J. Math. Sci. 15 (2001),
2373-2387.
[6] N. Boudi, H. Marhnine, and C. Zarhouti, Additive Derivations on Jordan Banach Pairs, Comm. in Algebra, Vol. 32 N. 9, (2004), pp. 3609-3625.
[7] W. Cortes and C. Haetinger, On Jordan generalized higher derivations on rings,
Turk. J. Math, 29 (2005), 1-10.
[8] M. Cabrera Garcia , A. Moreno Galindo, and A. Rodriguez Palacios, Zel'manov's theorem for primitive Banach-Jordan algebras, J. London Math. Soc. (2) 57 (1998) 231¬244.
[9] A. D'Amour ant K. McCrimmon, The Local algebra of Jordan Systems, J. Algebra
177 (1995), 199-239.
[10] A. Fernandez Lopez, H. Marhnine and C. Zarhouti, Derivations on Banach-Jordan
Pairs, Quart. J. Math. 3 (2001), 1-15.
[II] C. Haetinger, Higher derivations on Lie ideals, Tendencias em Matematica e com-
putacional 3 (2002),141-145.
[12] H. Hasse and F. K. Shmidt, Noch eine hegrüdung der theorie der hoheren Differential quotienten einem algehraischen Funtionenkorper einer Unhestimmeten, J. Reine
Angew Math. 177 (1937), 215-237.
[13] S. Hejazian and L. Shatery, Automatic continuity of higher derivations on JB* —algebras,
Bull. Iranian Math. Soc. Vol. 33, 1 (2007), pp 11-23.
[14] G. Hessenberger, Riesz und Fredholm-Theorie in Banach-Jordan Systemen, Uni-versitat Innsbruck, 1994.
[15] N. P. Jewell, Continuity of modules and higher derivations, Pacific J. Math. 68
(1977), 91-98.
[16] N. P. Jewell and A. M. Sinclair, Epimorphisms and derivations on L1(0,1) are continuous, Bull. London Math. Soc. 8 (1976) 135-139.
[17] K.W. Jun and Y.W. Lee, The image ofa continuous strong higher derivation is contained in the radical, Bull. Korean Math. Soc. 33 (1996), 229-232.
[18] O. Loos, Jordan pairs, Lecture Notes in Mathematics, Vol 460, Springer Verlag,
New York, 1975.
[19] O. Loos, Recent results on finiteness conditions in Jordan pairs, Jordan algebras, Proceedings of a conference in Overwolfach, 1992, De Gruyter, pp. 83-95.
H. Marhnine, C. Zarhouti / Eur. J. Pure Appl. Math, 10 (4) (2017), 749-762 762 [20] O. Loos Properly algebraic and spectrum-finite ideals in Jordan systems, Math.
Proc. Camb. Phil. Soc. (1993), 114, 149-161.
[21] O. Loos, Bounded symmetric domains and Jordan pairs, Lecture Notes , University of California, 1975.
[22] R. J. Loy, Continuity of higher derivations, Proc. Amer. Math. Soc. 37 (1973)
505-510.
[23] H. Marhnine, Caracterisation de certaines classes de paires de Banach-Jordan, These doctorale, Üniversite Abdelmalek Essaadi, Faculte des Sciences de Tetouan, Maroc
(2000).
[24] M. Mirzavaziri, Characterization of higher derivations on algebras , Comm. in
Algebra, 38 (2010), no 3, 981-987.
[25] F. Montaner, Local PI- Theory of Jordan systems, J. Algebra 216 (1999), 302-327. [26] J. M. Osborn and M. L. Racine, Jordan rings with nonzero socle, Trans. Amer.
Math. Soc. 251 (1979), 375-387.
[27] A. Roy and R. Sridharan, higher derivations and central simple algebras, Nagoya
Math. J. 32 (1968), 21-30.
[28] S. Sato, On rings with a higher derivation, Proc. Amer. Math. Soc. 30 (1971),
21-30.
[29] M. P. Thomas, Primitive ideals and derivations on noncommutative Banach alge¬bras, Pacific J. Math, 159 (1993) 139-152.
[30] Y. Uchino and T. Satoh, Function field modular forms and higher derivations,
Math. Ann. 311 (1998), 439-466.
[31] E. I. Zelmanov, Primary Jordan triple systems III, Sib. Math. J. 26 (1985), 55-64.

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