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Numerically hypercyclic polynomials
In this paper, we show that every complex Banach space X with dimension at least 2 supports a numerically hypercyclic d -homogeneous polynomial P for...
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Asplund Operators and p-Integral Polynomials
We introduce the Banach ideals of p -integral and of p -nuclear polynomials for 1 ≤ p ≤ + ∞ , extending to the polynomial setting the well known notions...
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Every Banach ideal of polynomials is compatible with an operator ideal
We show that for each Banach ideal of homogeneous polynomials, there exists a (necessarily unique) Banach operator ideal compatible with it....
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Hilbert–Schmidt and multiple summing operators
We characterize the multiple p -summing operators for p ≥ 2, in the situation where the range and some of the factors of the cartesian product are...
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The polynomial Daugavet property for atomless L 1(μ)-spaces
For any atomless positive measure μ , the space L 1 ( μ ) has the polynomial Daugavet property, i.e., every weakly compact continuous polynomial
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Dominated, diagonal polynomials on ℓ p spaces
We show that the r -dominated polynomials on ℓ p (2 ≦ p ≦ ∞) are integral on ℓ 1 , and give examples proving that the converse is not true. We...
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Extension and lifting of polynomials
We characterize the Banach spaces enjoying polynomial lifting properties, and the spaces that admit compact extensions of polynomials.