Abstract

In this chapter we will show some results on the extreme points of the unit ball of certain polynomial spaces in arbitrary Banach spaces. More particularly, we are interested in studying integral, nuclear and orthogonally additive polynomials.

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References

  1. Q. Bu, G. Buskes, Polynomials on Banach lattices and positive tensor products. J. Math. Anal. Appl. 388(2), 845–862 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  2. C. Boyd, S. Lassalle, Extreme and exposed points of spaces of integral polynomials. Proc. Am. Math. Soc. 138(4), 1415–1420 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. C. Boyd, R.A. Ryan, Geometric theory of spaces of integral polynomials and symmetric tensor products. J. Funct. Anal. 179(1), 18–42 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. C. Boyd, R.A. Ryan, N. Snigireva, Geometry of spaces of orthogonally additive polynomials on C(K). J. Geom. Anal. (2020). https://doi.org/10.1007/s12220-019-00240-0

  5. D. Carando, S. Lassalle, I. Zalduendo, Orthogonally additive polynomials over C(K) are measures—a short proof. Integral Equations Oper. Theory 56(4), 597–602 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. V. Dimant, D. Galicer, R. García, Geometry of integral polynomials, M-ideals and unique norm preserving extensions. J. Funct. Anal. 262(5), 1987–2012 (2012)

    MATH  Google Scholar 

  7. S. Dineen, Extreme integral polynomials on a complex Banach space. Math. Scand. 92(1), 129–140 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. S. Kakutani, Concrete representation of abstract (M)-spaces. (A characterization of the space of continuous functions.). Ann. Math. (2) 42, 994–1024 (1941)

    Google Scholar 

  9. R.A. Ryan, B. Turett, Geometry of spaces of polynomials. J. Math. Anal. Appl. 221(2), 698–711 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  10. M.A. Toumi, A decomposition of orthogonally additive polynomials on Archimedean vector lattices. Bull. Belg. Math. Soc. Simon Stevin 20(4), 621–638 (2013)

    Article  MathSciNet  MATH  Google Scholar 

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Ferrer, J., García, D., Maestre, M., Muñoz, G.A., Rodríguez, D.L., Seoane, J.B. (2022). Banach Spaces. In: Geometry of the Unit Sphere in Polynomial Spaces. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-031-23676-1_8

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