Equivalence of K -irreducibility concepts

Ivo Marek; Karel Žitný

Commentationes Mathematicae Universitatis Carolinae (1984)

  • Volume: 025, Issue: 1, page 61-72
  • ISSN: 0010-2628

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Marek, Ivo, and Žitný, Karel. "Equivalence of $K$-irreducibility concepts." Commentationes Mathematicae Universitatis Carolinae 025.1 (1984): 61-72. <http://eudml.org/doc/17298>.

@article{Marek1984,
author = {Marek, Ivo, Žitný, Karel},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {normal generating cone; equivalence of various concepts of irreducibility of positive operators in partially ordered Banach spaces},
language = {eng},
number = {1},
pages = {61-72},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Equivalence of $K$-irreducibility concepts},
url = {http://eudml.org/doc/17298},
volume = {025},
year = {1984},
}

TY - JOUR
AU - Marek, Ivo
AU - Žitný, Karel
TI - Equivalence of $K$-irreducibility concepts
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1984
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 025
IS - 1
SP - 61
EP - 72
LA - eng
KW - normal generating cone; equivalence of various concepts of irreducibility of positive operators in partially ordered Banach spaces
UR - http://eudml.org/doc/17298
ER -

References

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  1. BRUALDI R. A., PARTER S. V., SCHNEIDER H., The diagonal equivalence of a nonnegative matrix to a stochastic matrix, J. Math. Anal. Appl. 16 (1966), 31-50. (1966) Zbl0231.15017MR0206019
  2. FROBENIUS G., Über Matrizen aus nicht negativen Elementen, Sitzungsberichte Preuss. Akad. Wiss. Berlin 1912, 456-477. (1912) 
  3. GEIRINGER H., On the solution of systems of linear equations by certain iterative methods, Reissner Anniversary Volume, J. W. Edwards, Ann Arbor, Michigan 1949. (1949) 
  4. KÖNIG D., Theorie der endlichen und unendlichen Graphen, Chelsea Publ. Co., New York 1950. (1950) MR0036989
  5. KREIN M. G., RUTMAH M. A., Linear operators leaving a oone invariant in a Banach space, Uspekhi Mat. Nauk III, N 1 (1948), 3-95 (In Russian). English translation Amer. Math. Soc. Translations 26 (1950), 128 pp. (1948) MR0027128
  6. MARCUS M., MINC H., A Survey of Matrix Theory and Matrix Inequalities, Allyn and Bacon, Boston 1964; the Russian translation, Nauka Moscow 1972. (1964) Zbl0126.02404MR0162808
  7. MAREK I., Frobenius theory of positive operators, Comparison theorems and applications, SIAM J. Appl. Math. 19 (1970), 607-628. (1970) Zbl0219.47022MR0415405
  8. SAHASHIMA I., Spectral properties of some positive operators, Natur. Sci. Rep. Ochanomizu Univ. 15 (1964), 55-64. (1964) MR0187096
  9. SCHAFFER H. H., Spectral properties of positive linear transformations, Pacif. J. Math. 10 (1960), 1009-1019. (1960) MR0115090
  10. SCHNEIDER H., The concepts of irreducibility and full indecomposabillty of a matrix in the works of Frobenius, König and Markov, Lin. Algebra and Its Applications 18 (1977), 139-162. (1977) MR0446850
  11. STECENKO V. Ya., Criteria of irreducibility of linear operators, Uspekhi Mat. Nauk XXI, Nr. 5 (131) (1966), 265-266 (Russian). (1966) MR0201977
  12. VANDERGRAFT J. S., Spectral properties of matrices which have invariant cones, SIAM J. Appl. Math. 16 (1968), 1208-1222. (1968) Zbl0186.05701MR0244284
  13. VARGA R. S., Matrix Iterative Analysis, Prentice Hall Inc. Englewood Cliffs, New Jersey, 1962. (1962) MR0158502

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