Abstract

We introduce the concepts of Cohen positive strongly p -summing and positive p -dominated m-homogeneous polynomials. The version of Pietsch’s domination theorem for the first class among other results and a Bu-type theorem is proved, as well as some inclusions with other known spaces. Moreover, we present a characterization of these classes in tensor terms.

Highlights

  • We give a natural generalization of the notion of Cohen positive strongly p− summing to the category of homogeneous polynomial mappings

  • We introduce the notion of Cohen positive strongly p− summing m− homogeneous polynomials, and we study some fundamental properties

  • E following theorem is a version of the Bu-theorem [12]; in [13], Achour and Mezrag proved an inclusion theorem between p-dominated operators and Cohen strongly q-summing m− linear operators; in our work, we prove a positive analogue of eorem 3.2 in [13]. is theorem plays an important role in the proof of the relationship between Cohen positive strongly summing and positive dominated polynomials

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Summary

Cohen Positive Strongly p-Summing m-Homogeneous Polynomials

We give a natural generalization of the notion of Cohen positive strongly p− summing to the category of homogeneous polynomial mappings. An m− homogeneous polynomial P: X ⟶ F is Cohen positive strongly p− summing (1 < p ≤ + ∞) if and only if there is a Radon probability measure μ on B+F∗∗, such that, for all x ∈ X and y∗ ∈ F∗, we have. Is Cohen positive strongly p− summing, its associated symmetric m− linear operator P􏽢 ∈ P(mX; F) is multiple p− convex. If the polynomial P ∈ P(mX; c0) is Cohen positive strongly p− summing, its associated symmetric m− linear operator P􏽢 is in L(mX; c0). E following properties are equivalent (i) e polynomial P belongs to P+coh,p(mX; F) (ii) e operator P􏽥 belongs to D+p(􏽣⊗ mπ,sX; F) (iii) ∃Z is a Banach space, u ∈ D+p(Z, F), and.

Positive p-Dominated mHomogeneous Polynomials
Applications
Conclusion
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