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Inner derivations
on ultraprime normed algebras


Authors: M. Cabrera and J. Martínez
Journal: Proc. Amer. Math. Soc. 125 (1997), 2033-2039
MSC (1991): Primary 47B47; Secondary 47B48, 46H05
DOI: https://doi.org/10.1090/S0002-9939-97-03833-1
MathSciNet review: 1389506
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Abstract: We show that, for every ultraprime Banach algebra $A$, there exists a positive number $\gamma $ satisfying $\gamma \|a+Z(A)\|\le \|D_a\|$ for all $a$ in $A$, where $Z(A)$ denotes the centre of $A$ and $D_a$ denotes the inner derivation on $A$ induced by $a$. Moreover, the number $\gamma $ depends only on the ``constant of ultraprimeness'' of $A$.


References [Enhancements On Off] (What's this?)

  • 1. P. Ara and M. Mathieu, On ultraprime Banach algebras with non-zero socle, Proc. Roy. Irish Acad. 91A (1991), 89-98. MR 93h:46061
  • 2. M. Cabrera and A. Rodríguez, Non-degenerately ultraprime Jordan-Banach algebras: A Zel$'$manovian treatment, Proc. London Math. Soc. 69 (1994), 576-604. MR 95g:46094
  • 3. L. A. Fialkow, Structural properties of elementary operators, in Elementary operators and applications, Proc. Int. Workshop, Blaubeuren, June 1991; World Scientific, Singapore, 1992, 55-113. MR 93i:47042
  • 4. B. E. Johnson, Norms of derivations on $\mathcal L(\mathcal X)$, Pacific J. Math. 38 (1971), 465-469. MR 46:6087
  • 5. J. Kyle, Norms of derivations, J. London Math. Soc. 16 (1977), 297-312. MR 58:7113
  • 6. M. Mathieu, Rings of quotients of ultraprime Banach algebras with applications to elementary operators, Proc. Centre Math. Anal. Austral. Nat. Univ. 21 (1989), 297-317. MR 91a:46054
  • 7. -, Elementary operators on prime $C^*$-algebras, I. Math. Ann. 284 (1989), 223-244. MR 90h:46092
  • 8. -, The symmetric algebra of quotients of an ultraprime Banach algebra, J. Austral. Math. Soc. Ser. A 50 (1991), 75-87. MR 92g:46061
  • 9. -, The $cb$-norm of a derivation, in Algebraic methods in operator theory, ed. R. E. Curto and P. E. T. Jorgensen, Birkhauser, Basel-Boston, 1994, pp. 144-152. MR 95g:46128
  • 10. D. W. B. Somerset, Inner derivations and primal ideals of $C^*$-algebras, J. London Math. Soc. 50 (1994), 568-580. MR 95h:46107
  • 11. G. J. Stampfli, The norm of a derivation, Pacific J. Math. 33 (1970), 737-747. MR 42:861

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Additional Information

M. Cabrera
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071-Granada, Spain
Email: cabrera@goliat.ugr.es

J. Martínez
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071-Granada, Spain
Email: jmmoreno@goliat.ugr.es

DOI: https://doi.org/10.1090/S0002-9939-97-03833-1
Received by editor(s): September 26, 1995
Received by editor(s) in revised form: January 24, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society

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