On quasipositive elements in ordered Banach algebras

Gerd Herzog; Roland Lemmert

Studia Mathematica (1998)

  • Volume: 129, Issue: 1, page 59-65
  • ISSN: 0039-3223

Abstract

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Let a real Banach algebra A with unit be ordered by an algebra cone K. We study the elements a ∈ A with exp(ta) ∈ K, t≥ 0.

How to cite

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Herzog, Gerd, and Lemmert, Roland. "On quasipositive elements in ordered Banach algebras." Studia Mathematica 129.1 (1998): 59-65. <http://eudml.org/doc/216492>.

@article{Herzog1998,
abstract = {Let a real Banach algebra A with unit be ordered by an algebra cone K. We study the elements a ∈ A with exp(ta) ∈ K, t≥ 0.},
author = {Herzog, Gerd, Lemmert, Roland},
journal = {Studia Mathematica},
keywords = {real Banach algebra with unit; ordered by an algebra cone},
language = {eng},
number = {1},
pages = {59-65},
title = {On quasipositive elements in ordered Banach algebras},
url = {http://eudml.org/doc/216492},
volume = {129},
year = {1998},
}

TY - JOUR
AU - Herzog, Gerd
AU - Lemmert, Roland
TI - On quasipositive elements in ordered Banach algebras
JO - Studia Mathematica
PY - 1998
VL - 129
IS - 1
SP - 59
EP - 65
AB - Let a real Banach algebra A with unit be ordered by an algebra cone K. We study the elements a ∈ A with exp(ta) ∈ K, t≥ 0.
LA - eng
KW - real Banach algebra with unit; ordered by an algebra cone
UR - http://eudml.org/doc/216492
ER -

References

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  1. [1] G. P. Barker, On matrices having an invariant cone, Czechoslovak Math. J. 22 (1972), 49-68. Zbl0238.15005
  2. [2] F. F. Bonsall, and J.Duncan, Complete Normed Algebras, Springer, 1973. Zbl0271.46039
  3. [3] H.-J. Krieger, Beiträge zur Theorie positiver Operatoren, Akademie-Verlag, Berlin, 1969. 
  4. [4] R. Loewy and H. Schneider, Positive operators on the n-dimensional ice cream cone, J. Math. Anal. Appl. 49 (1975), 375-392. Zbl0308.15011
  5. [5] H. Raubenheimer and D. Rode, Cones in Banach algebras, Indag. Math. 7 (1996), 489-502. 
  6. [6] R. Redheffer and W. Walter, Flow-invariant sets and differential inequalities in normed spaces, Appl. Anal. 5 (1975), 149-161. Zbl0353.34067
  7. [7] H. H. Schaefer, Topological Vector Spaces, Springer, 1980. 
  8. [8] P. Volkmann, Gewöhnliche Differentialungleichungen mit quasimonoton wachsenden Funktionen in topologischen Vektorräumen, Math. Z. 127 (1972), 157-164. Zbl0226.34058
  9. [9] P. Volkmann, Über die Invarianz konvexer Mengen und Differentialungleichungen in einem normierten Raume, Math. Ann. 203 (1973), 201-210. Zbl0251.34039

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