Minimal incomplete norms on Banach algebras

Michael Meyer

Studia Mathematica (1992)

  • Volume: 102, Issue: 1, page 77-85
  • ISSN: 0039-3223

Abstract

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We study the family of all not necessarily complete algebra norms on a semisimple Banach algebra as a partially ordered set and investigate the existence and properties of minimal elements.

How to cite

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Meyer, Michael. "Minimal incomplete norms on Banach algebras." Studia Mathematica 102.1 (1992): 77-85. <http://eudml.org/doc/215915>.

@article{Meyer1992,
abstract = {We study the family of all not necessarily complete algebra norms on a semisimple Banach algebra as a partially ordered set and investigate the existence and properties of minimal elements.},
author = {Meyer, Michael},
journal = {Studia Mathematica},
keywords = {Banach algebras; norms; spectral radius; algebra norms on a semisimple Banach algebra; existence and properties of minimal elements},
language = {eng},
number = {1},
pages = {77-85},
title = {Minimal incomplete norms on Banach algebras},
url = {http://eudml.org/doc/215915},
volume = {102},
year = {1992},
}

TY - JOUR
AU - Meyer, Michael
TI - Minimal incomplete norms on Banach algebras
JO - Studia Mathematica
PY - 1992
VL - 102
IS - 1
SP - 77
EP - 85
AB - We study the family of all not necessarily complete algebra norms on a semisimple Banach algebra as a partially ordered set and investigate the existence and properties of minimal elements.
LA - eng
KW - Banach algebras; norms; spectral radius; algebra norms on a semisimple Banach algebra; existence and properties of minimal elements
UR - http://eudml.org/doc/215915
ER -

References

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  1. [1] B. Aupetit, The uniqueness of the complete norm topology in Banach algebras and Banach Jordan algebras, J. Funct. Anal. 47 (1982), 1-6. Zbl0488.46043
  2. [2] F. F. Bonsall, A minimal property of the norm in some Banach algebras, J. London Math. Soc. 29 (1954), 156-164. 
  3. [3] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, Berlin 1973. Zbl0271.46039
  4. [4] S. B. Cleveland, Homomorphisms of non-commutative *-algebras, Pacific J. Math. 13 (1963), 1097-1109. Zbl0205.42203
  5. [5] J. Esterle, Normes d'algèbres minimales, topologie d'algèbre normée minimum sur certaines algèbres d'endomorphismes continus d'un espace normé, C. R. Acad. Sci. Paris Sér. A 277 (1973), 425-427. Zbl0268.46045
  6. [6] M. J. Meyer, Minimal norms on SQDZ-Banach algebras, Proc. Roy. Irish Acad. 89A (1989), 127-133. Zbl0665.46041
  7. [7] M. J. Meyer, The spectral extension property and extension of multiplicative linear functionals, Proc. Amer. Math. Soc. 112 (1991), 855-861. Zbl0744.46041
  8. [8] T. W. Palmer, Spectral algebras, subalgebras and pseudonorms, Rocky Mountain J. Math., to appear. 
  9. [9] T. J. Ransford, A short proof of Johnson's theorem, Bull. London Math. Soc. 21 (1989), 487-488. Zbl0705.46028
  10. [10] C. E. Rickart, General Theory of Banach Algebras, Krieger, New York 1960. Zbl0095.09702
  11. [11] Á. Rodríguez-Palacios, Automatic continuity with application to C*-algebras, Math. Proc. Cambridge Philos. Soc., to appear. Zbl0762.46052
  12. [12] B. J. Tomiuk and B. Yood, Incomplete normed algebra norms on Banach algebras, Studia Math. 95 (1989), 119-132. Zbl0715.46024
  13. [13] B. Yood, Homomorphisms on normed algebras, Pacific J. Math. 8 (1958), 373-381. Zbl0084.33601

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