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1999 | 136 | 1 | 91-97
Tytuł artykułu

The triple-norm extension problem: the nondegenerate complete case.

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove that, if A is an associative algebra with two commuting involutions τ and π, if A is a τ-π-tight envelope of the Jordan Triple System T:=H(A,τ) ∩ S(A,π), and if T is nondegenerate, then every complete norm on T making the triple product continuous is equivalent to the restriction to T of an algebra norm on A.
Czasopismo
Rocznik
Tom
136
Numer
1
Strony
91-97
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-11-13
Twórcy
  • Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain, agalindo@goliat.ugr.es
Bibliografia
  • [ACCM] J. A. Anquela, T. Cortés, K. McCrimmon and F. Montaner, Strong primeness of hermitian Jordan systems, J. Algebra 198 (1997), 311-326.
  • [CMR1] M. Cabrera, A. Moreno and A. Rodríguez, On the behaviour of Jordan-algebra norms on associative algebras, Studia Math. 113 (1995), 81-100.
  • [CMR2] M. Cabrera, A. Moreno and A. Rodríguez, Normed versions of the Zel'manov prime theorem: positive results and limits, in: In Operator Theory, Operator Algebras and Related Topics (Timişoara, 1996), A. Gheondea, R. N. Gologan, and D. Timotin (eds.), The Theta Foundation, Bucharest, 1997, 65-77.
  • [CMR3] M. Cabrera, A. Moreno and A. Rodríguez, Zel'manov theorem for primitive Jordan-Banach algebras, J. London Math. Soc. (2) 57 (1998), 231-244.
  • [CMRZ] M. Cabrera, A. Moreno, A. Rodríguez and E. Zel'manov, Jordan polynomials can be analytically recognized, Studia Math. 117 (1996), 137-147.
  • [CR1] M. Cabrera and A. Rodríguez, Zel'manov theorem for normed simple Jordan algebras with a unit, Bull. London Math. Soc. 25 (1993), 59-63.
  • [CR2] M. Cabrera and A. Rodríguez, Nondegenerately ultraprime Jordan-Banach algebras: a Zel'manovian treatment, Proc. London Math. Soc. 69 (1994), 576-604.
  • [D'A] A. D'Amour, Quadratic Jordan systems of hermitian type, J. Algebra 149 (1992), 197-233.
  • [D'AM] A. D'Amour and K. McCrimmon, The structure of quadratic Jordan systems of Clifford type, submitted to J. Algebra.
  • [FGR] A. Fernández, E. García and A. Rodríguez, A Zel'manov prime theorem for JB*-algebras, J. London Math. Soc. 46 (1992), 319-335.
  • [Mor1] A. Moreno, Distinguishing Jordan polynomials by means of a single Jordan-algebra norm, Studia Math. 122 (1997), 67-73.
  • [Mor2] A. Moreno, Extending the norm from special Jordan Triple Systems to their associative envelope, in: Banach Algebras'97, E. Albrecht and M. Mathieu (eds.), de Gruyter, Berlin, 1998, 363-375.
  • [MR1] A. Moreno and A. Rodríguez, The norm extension problem: positive results and limits, Extracta Math. 12 (1997), 165-171.
  • [MR2] A. Moreno and A. Rodríguez, Algebra norms on tensor products of algebras and the norm extension problem, Linear Algebra Appl. 269 (1998), 257-305.
  • [Rod1] A . Rodríguez, Jordan structures in Analysis, in: Jordan Algebras (Oberwolfach, 1992), W. Kaup, K. McCrimmon, and H. Petersson (eds.), de Gruyter, Berlin, 1994, 97-186.
  • [RSZ] A. Rodríguez, A. Slin'ko and E. Zel'manov, Extending the norm from Jordan-Banach algebras of hermitian elements to their associative envelopes, Comm. Algebra 22 (1994), 1435-1455.
  • [Zel1] E. I. Zel'manov, On prime Jordan algebras II, Sibirsk. Mat. Zh. 24 (1983), no. 1, 89-104 (in Russian).
  • [Zel2] E. I. Zel'manov, On prime Jordan triple systems, ibid. 24 (1983), no. 4, 23-37 (in Russian).
  • [Zel3] E. I. Zel'manov, On prime Jordan triple systems II, ibid. 25 (1984), no. 5, 50-61 (in Russian).
  • [Zel4] E. I. Zel'manov, On prime Jordan triple systems III, ibid. 26 (1985), no. 1, 71-82 (in Russian).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv136i1p91bwm
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