Approximate determination of spectral radius of a positive irreducible operator

Ivo Marek

Aplikace matematiky (1967)

  • Volume: 12, Issue: 5, page 351-363
  • ISSN: 0862-7940

Abstract

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Beiderseitige Schranken für den Spektralradius einer spaziellen Klasse von Abbildungen die einen Kegel der nichtnegativen Elemente eines Banachraumes reproduzieren, sind angeben. Mit Hilfe des verallgemeinerten Minimaxprinzips wird einerseits der Collatz'sche Quotientensatz und andererseits das Prinzip von Yamamoto verallgemeinert.

How to cite

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Marek, Ivo. "Přibližné stanovení spektrálního poloměru kladného nerozložitelného zobrazení." Aplikace matematiky 12.5 (1967): 351-363. <http://eudml.org/doc/14492>.

@article{Marek1967,
author = {Marek, Ivo},
journal = {Aplikace matematiky},
keywords = {functional analysis},
language = {cze},
number = {5},
pages = {351-363},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Přibližné stanovení spektrálního poloměru kladného nerozložitelného zobrazení},
url = {http://eudml.org/doc/14492},
volume = {12},
year = {1967},
}

TY - JOUR
AU - Marek, Ivo
TI - Přibližné stanovení spektrálního poloměru kladného nerozložitelného zobrazení
JO - Aplikace matematiky
PY - 1967
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 12
IS - 5
SP - 351
EP - 363
LA - cze
KW - functional analysis
UR - http://eudml.org/doc/14492
ER -

References

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  1. E. Bohl, 10.1007/BF00285424, Arch. Rat. Mech. Anal. 22 (1966), 313-332. (1966) Zbl0232.65047MR0234305DOI10.1007/BF00285424
  2. L. Collatz, 10.1007/BF01180971, Math. Zeitschr. 47(1942), 395-398. (1942) MR0007086DOI10.1007/BF01180971
  3. L. Collatz, 10.1007/BF01180013, Math. Zeitschr. 48 (1942 - 43), 221-226. (1942) MR0008590DOI10.1007/BF01180013
  4. K. P. Hadeler, Einschliessungssätze bei normalen und bei positiven Operatoren, Arch. Rat. Mech. Anal. 21 (1966), 58 - 88. (1966) Zbl0151.20101MR0187090
  5. A. S. Householder, The Theory of Matrices in Numerical Analysis, Blaisdell Publ. New York 1964. (1964) Zbl0161.12101MR0175290
  6. M. А. Красносельский, Положительные решения операторных уравнений, Гостехиздат, Москва 1962. (1962) Zbl1005.68507
  7. M. Г. Крейн M. А. Рутман, Линейные операторы оставляющие инвариантным конус в пространстве Банаха, Усп. мат. наук /(1948), No. 1, 3-95. (1948) Zbl1154.94303MR0027128
  8. I. Marek, An infinite dimensional analogue of R. S. Varga's lemma, Comment. Math. Univ. Carolinae 8, 1 (1967), 27-38. (1967) Zbl0169.17201MR0232263
  9. I. Marek, Iterations of linear bounded operators and Kellogg's iterations in non self-adjoint eigenvalue problems, Czech. Math. Journ. 12 (1962), 536-554. (1962) MR0149297
  10. I. Marek, Некоторые математические задачи теории ядерных реакторов на быстрых нейтронах, Aplikace matematiky 8 (1963), 442-470. (1963) Zbl0201.16704
  11. I. Marek, Positivität und kritischer Zustand, Vorträge der 3. Tagung über Probleme und Methoden der Mathematischen Physik. Karl-Marx-Stadt 1966, 191-205. (1966) Zbl0174.44504
  12. I. Marek, Spektraleigenschaften der χ -positiven Operatoren und Einschliessungssätze für den Spektralradius, Czech. Math. Journ. 16(1966), 493-517. (1966) MR0217622
  13. I. Marek, u 0 -positive operators and some of their applications, Journ. Soc. Industr. Appl. Math. 15 (1967), No. 3, 384-394. (1967) MR0233176
  14. F. Niiro I. Sawashima, On the spectral properties of positive irreducible operators in an arbitrary Banach lattice and problem of H. H. Schaefer, Sci. Pap. Coll. Gen. Education, Univ. of Tokyo, 16 (1966), 145-183. (1966) MR0205084
  15. I. Sawashima, On spectral properties of some positive operators, Nat. Sci. Rep. of the Ochanomizu Univ. 15 (1964), 53-64. (1964) Zbl0138.07801MR0187096
  16. A. E. Taylor, Introduction to Functional Analysis, J. Wiley, Publ., New York 1958. (1958) Zbl0081.10202MR0098966
  17. R. S. Varga, Matrix Iterative Analysis, Prentice-Hall Inc. Englewood Cliffs, New Jersey 1962. (1962) MR0158502
  18. T. Yamamoto, 10.1007/BF02162977, Numer. Math. 8 (1966), 324-333. (1966) Zbl0163.38801MR0218011DOI10.1007/BF02162977

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