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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Uniform primeness of the Jordan algebra of symmetric operators
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by L. L. Stachó and B. Zalar PDF
Proc. Amer. Math. Soc. 126 (1998), 2241-2247 Request permission

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.
References
  • 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, DOI 10.1112/plms/s3-69.3.576
  • Seán Dineen, The Schwarz lemma, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1989. Oxford Science Publications. MR 1033739
  • J. Faraut and A. Koranyi, Analysis on Symmetric Cones, Oxford Press, 1994.
  • 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
  • Nathan Jacobson, Structure and representations of Jordan algebras, American Mathematical Society Colloquium Publications, Vol. XXXIX, American Mathematical Society, Providence, R.I., 1968. MR 0251099, DOI 10.1090/coll/039
  • Wilhelm Kaup and Kevin McCrimmon (eds.), Jordan algebras, Walter de Gruyter & Co., Berlin, 1994. MR 1293311, DOI 10.1515/9783110878110
  • Ottmar Loos, Jordan pairs, Lecture Notes in Mathematics, Vol. 460, Springer-Verlag, Berlin-New York, 1975. MR 0444721, DOI 10.1007/BFb0080843
  • O. Loos, Bounded Symmetric Domains and Jordan Pairs, University of California at Irvine, 1977.
  • James D. Malley, Statistical applications of Jordan algebras, Lecture Notes in Statistics, vol. 91, Springer-Verlag, New York, 1994. MR 1308501, DOI 10.1007/978-1-4612-2678-9
  • 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, DOI 10.1017/S0004972700028203
  • Erhard Neher, Jordan triple systems by the grid approach, Lecture Notes in Mathematics, vol. 1280, Springer-Verlag, Berlin, 1987. MR 911879, DOI 10.1007/BFb0078217
  • Ichirô Satake, Algebraic structures of symmetric domains, Kanô Memorial Lectures, vol. 4, Iwanami Shoten, Tokyo; Princeton University Press, Princeton, N.J., 1980. MR 591460
  • Tonny Albert Springer, Jordan algebras and algebraic groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 75, Springer-Verlag, New York-Heidelberg, 1973. MR 0379618
  • 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
  • Harald Upmeier, Symmetric Banach manifolds and Jordan $C^\ast$-algebras, North-Holland Mathematics Studies, vol. 104, North-Holland Publishing Co., Amsterdam, 1985. Notas de Matemática [Mathematical Notes], 96. MR 776786
  • 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, DOI 10.1090/cbms/067
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Additional Information
  • L. L. Stachó
  • Affiliation: Bolyai Intézet, Aradi Vértanuk tere 1, 6720 Szeged, Hungary
  • Email: stacho@math.u-szeged.hu
  • B. Zalar
  • Affiliation: University of Maribor, Faculty of Civil Engineering, Department of Basic Sciences, Smetanova 17, 62000 Maribor, Slovenija
  • Email: borut.zalar@uni-mb.si or borut.zalar@uni-lj.si
  • Received by editor(s): January 19, 1996
  • Communicated by: Palle E. T. Jorgensen
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 2241-2247
  • MSC (1991): Primary 46L70, 15A45, 15A60, 16W10, 17C65
  • DOI: https://doi.org/10.1090/S0002-9939-98-04769-8
  • MathSciNet review: 1487342