Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Uniform primeness of the Jordan algebra
of symmetric operators

Authors: L. L. Stachó and B. Zalar
Journal: Proc. Amer. Math. Soc. 126 (1998), 2241-2247
MSC (1991): Primary 46L70, 15A45, 15A60, 16W10, 17C65
MathSciNet review: 1487342
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Abstract | References | Similar Articles | Additional Information

Abstract: In this note we establish the best possible constant for the general lower estimate for the Jacobson - McCrimmon operator on the algebra of symmetric operators acting on a Hilbert space.

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  • 1. M. Cabrera García and Á. Rodríguez-Palacios, Non-degenerately ultraprime Jordan-Banach algebras: a Zel′manovian treatment, Proc. London Math. Soc. (3) 69 (1994), no. 3, 576–604. MR 1289864, 10.1112/plms/s3-69.3.576
  • 2. Seán Dineen, The Schwarz lemma, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1989. Oxford Science Publications. MR 1033739
  • 3. J. Faraut and A. Koranyi, Analysis on Symmetric Cones, Oxford Press, 1994. CMP 97:12
  • 4. José-M. Isidro and László L. Stachó, Holomorphic automorphism groups in Banach spaces: an elementary introduction, North-Holland Mathematics Studies, vol. 105, North-Holland Publishing Co., Amsterdam, 1985. Notas de Matemática [Mathematical Notes], 97. MR 779821
  • 5. Nathan Jacobson, Structure and representations of Jordan algebras, American Mathematical Society Colloquium Publications, Vol. XXXIX, American Mathematical Society, Providence, R.I., 1968. MR 0251099
  • 6. Wilhelm Kaup and Kevin McCrimmon (eds.), Jordan algebras, Walter de Gruyter & Co., Berlin, 1994. MR 1293311
  • 7. Ottmar Loos, Jordan pairs, Lecture Notes in Mathematics, Vol. 460, Springer-Verlag, Berlin-New York, 1975. MR 0444721
  • 8. O. Loos, Bounded Symmetric Domains and Jordan Pairs, University of California at Irvine, 1977.
  • 9. James D. Malley, Statistical applications of Jordan algebras, Lecture Notes in Statistics, vol. 91, Springer-Verlag, New York, 1994. MR 1308501
  • 10. Martin Mathieu, More properties of the product of two derivations of a 𝐶*-algebra, Bull. Austral. Math. Soc. 42 (1990), no. 1, 115–120. MR 1066365, 10.1017/S0004972700028203
  • 11. Erhard Neher, Jordan triple systems by the grid approach, Lecture Notes in Mathematics, vol. 1280, Springer-Verlag, Berlin, 1987. MR 911879
  • 12. Ichirô Satake, Algebraic structures of symmetric domains, Kanô Memorial Lectures, vol. 4, Iwanami Shoten, Tokyo; Princeton University Press, Princeton, N.J., 1980. MR 591460
  • 13. Tonny Albert Springer, Jordan algebras and algebraic groups, Springer-Verlag, New York-Heidelberg, 1973. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 75. MR 0379618
  • 14. L. L. Stachó and B. Zalar, On the norm of Jordan elementary operators in standard operator algebras, Publ. Math. Debrecen 49 (1996), no. 1-2, 127–134. MR 1416312
  • 15. Harald Upmeier, Symmetric Banach manifolds and Jordan 𝐶*-algebras, North-Holland Mathematics Studies, vol. 104, North-Holland Publishing Co., Amsterdam, 1985. Notas de Matemática [Mathematical Notes], 96. MR 776786
  • 16. Harald Upmeier, Jordan algebras in analysis, operator theory, and quantum mechanics, CBMS Regional Conference Series in Mathematics, vol. 67, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1987. MR 874756

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Additional Information

L. L. Stachó
Affiliation: Bolyai Intézet, Aradi Vértanuk tere 1, 6720 Szeged, Hungary

B. Zalar
Affiliation: University of Maribor, Faculty of Civil Engineering, Department of Basic Sciences, Smetanova 17, 62000 Maribor, Slovenija
Email: or

Keywords: Hilbert space, bounded operators, symmetric operators, Jordan algebra, Jacobson-McCrimmon operator, prime algebra
Received by editor(s): January 19, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society