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
Summary
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Similar Papers
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.