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Quadratic Operators in Banach Spaces and Nonassociative Banach Algebras

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Book cover Advances in Structured Operator Theory and Related Areas

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 237))

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Abstract

A survey of a general theory of quadratic operators in Banach spaces with close relations to the nonassociative Banach algebras is presented. Some applications to matrix and integral quadratic operators in classical Banach spaces are given.

Mathematics Subject Classification (2010). 46H70, 45G10

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References

  1. S.N. Bernstein. Solution of a mathematical problem related to the theory of inheritance, Uchenye Zapiski n.-i. kafedr Ukrainy 1 (1924), 83–115 (in Russian).

    Google Scholar 

  2. N. Bourbaki. Éléments de mathématique, Algèbre, Ch. 9: Formes sesquilinéaires et formes quadratiques, Hermann, Paris, 1959 (in French).

    Google Scholar 

  3. N. Danford and J.T. Schwartz. Linear operators, Part 1: General theory, Intersci. Publ., 1958.

    Google Scholar 

  4. M. Day. Normed linear spaces, Springer-Verlag, 1958.

    Google Scholar 

  5. P. Enflo. A counterexample to the approximation problem in Banach spaces, Acta Math. 130( 1973), 309–317.

    Article  MathSciNet  MATH  Google Scholar 

  6. I.M.H. Etherington. Genetic algebras, Proc. Roy. Soc. Edinburgh, A 59 (1939), 242– 258.

    Google Scholar 

  7. V.I. Glivenko. Mendelian algebra, Doklady Akad. Nauk SSSR 8, No.4 (1936), 371– 372 (in Russian).

    Google Scholar 

  8. J.C. Gutiérrez. Solution of the Bernstein problem in the non-regular case, J. Algebra 223, No.1 (2000), 226–132.

    Google Scholar 

  9. P. Holgate. Genetic algebras satisfying Bernstein’s stationarity principle. J. London Math. Soc. (2) 9 (1975), 612–624.

    Google Scholar 

  10. Yu.I. Lyubich. Basis concepts and theorems of evolutionary genetics for free populations, Russian Math. Surveys 26, No. 5 (1971), 51–123.

    Google Scholar 

  11. Yu.I. Lyubich, Two-level Bernstein populations, Math. USSR Sb. 24, No. 1 (1974), 593–615.

    Google Scholar 

  12. Yu.I. Lyubich. Proper Bernstein populations, Probl. Inform. Transmiss. (1978), 228– 235.

    Google Scholar 

  13. Yu.I. Lyubich. Bernstein algebras, Uspekhi Mat. Nauk 32, No. 6 (1977), 261–263 (in Russian).

    Google Scholar 

  14. Yu.I. Lyubich. Mathematical structures in population genetics, Springer-Verlag, 1992. (Translated from the Russian original, 1983, Naukova Dumka.)

    Google Scholar 

  15. Yu.I. Lyubich. Banach–Bernstein algebras and their applications. Nonassociative algebra and its applications, Lecture Notes in Pure and Appl. Math., 211, Dekker, 2000, pp. 205–210.

    Google Scholar 

  16. Yu.I. Lyubich. A theorem on Bernstein quadratic integral operators, Nonassociative algebra and its applications, Lect. Notes Pure and Appl. Math., 246, Chapman–Hall, 2006, pp. 245–251.

    Google Scholar 

  17. L. Nirenberg. Topics in nonlinear functional analysis, Courant Inst, 1974.

    Google Scholar 

  18. O. Reiersöl. Genetic algebras studied recursively and by means of differential operators, Math. Scand., 10( 1962), 25–44.

    MathSciNet  MATH  Google Scholar 

  19. A.S. Serebrovskii. Properties of Mendelian equalities, Doklady Akad. Nauk SSSR 2, No. 1 (1934), 33–36.

    Google Scholar 

  20. R.D. Schafer. An introduction to nonassociative algebras, Acad. Press, 1966.

    MATH  Google Scholar 

  21. A. Wörz-Busekros. Algebras in Genetics, Springer-Verlag, 1980.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Technion, 32000, Haifa, Israel

    Yu. I. Lyubich

Authors
  1. Yu. I. Lyubich
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Corresponding author

Correspondence to Yu. I. Lyubich .

Editor information

Editors and Affiliations

  1. Computer Sciences, Free University Amsterdam, Amsterdam, Noord-Holland, The Netherlands

    Marinus A. Kaashoek

  2. Department of Mathematics, College of William and Mary, Williamsburg, Virginia, USA

    Leiba Rodman

  3. Mathematics Department, Drexel University, Philadelphia, Pennsylvania, USA

    Hugo J. Woerdeman

Additional information

Dedicated to Leonia Lerer on the occasion of his 70th birthday

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Lyubich, Y.I. (2013). Quadratic Operators in Banach Spaces and Nonassociative Banach Algebras. In: Kaashoek, M., Rodman, L., Woerdeman, H. (eds) Advances in Structured Operator Theory and Related Areas. Operator Theory: Advances and Applications, vol 237. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0639-8_14

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