Displaying similar documents to “Integral polynomials on Banach spaces not containing ℓ 1 ”

Polynomials and geometry of Banach spaces.

Joaquín M. Gutiérrez, Jesús A. Jaramillo, José G. Llavona (1995)

Extracta Mathematicae

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In this paper we survey a large part of the results on polynomials on Banach spaces that have been obtained in recent years. We mainly look at how the polynomials behave in connection with certain geometric properties of the spaces.

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.

Ideals of homogeneous polynomials and weakly compact approximation property in Banach spaces

Erhan Çalışkan (2007)

Czechoslovak Mathematical Journal

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We show that a Banach space E has the weakly compact approximation property if and only if each continuous Banach-valued polynomial on E can be uniformly approximated on compact sets by homogeneous polynomials which are members of the ideal of homogeneous polynomials generated by weakly compact linear operators. An analogous result is established also for the compact approximation property.

Polynomial characterizations of Banach spaces not containing l.

Joaquín M. Gutiérrez (1991)

Extracta Mathematicae

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Many properties of Banach spaces can be given in terms of (linear bounded) operators. It is natural to ask if they can also be formulated in terms of polynomial, holomorphic and continuous mappings. In this note we deal with Banach spaces not containing an isomorphic copy of l, the space of absolutely summable sequences of scalars.

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.