Displaying similar documents to “On polynomial equations in Banach space, perturbation techniques and applications.”

Separating polynomials on Banach spaces.

R. Gonzalo, J. A. Jaramillo (1997)

Extracta Mathematicae

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In this paper we survey some recent results concerning separating polynomials on real Banach spaces. By this we mean a polynomial which separates the origin from the unit sphere of the space, thus providing an analog of the separating quadratic form on Hilbert space.

Integral polynomials on Banach spaces not containing ℓ 1

Raffaella Cilia, Joaquín M. Gutiérrez (2010)

Czechoslovak Mathematical Journal

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We give new characterizations of Banach spaces not containing ℓ 1 in terms of integral and p -dominated polynomials, extending to the polynomial setting a result of Cardassi and more recent results of Rosenthal.

Local polynomials are polynomials

C. Fong, G. Lumer, E. Nordgren, H. Radjavi, P. Rosenthal (1995)

Studia Mathematica

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We prove that a function f is a polynomial if G◦f is a polynomial for every bounded linear functional G. We also show that an operator-valued function is a polynomial if it is locally a polynomial.