Dominated multilinear operators defined on tensor products of Banach spaces
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Date
2022
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Publisher
Université de M'sila
Abstract
In this paper, we introduce and study new classes of dominated multilinear operators,
which we call ðp; p1; . . .; pn;G1; . . .;GnÞ-dominated and
ð ~ p; p1; . . .; pn;G1; . . .;GnÞ-dominated multilinear operators defined on the tensor
product of Banach spaces. Some characterizations of this type of operators are given
and we prove some important coincidence results. As an application, we characterize
ðp; p1; . . .; pnÞ-dominated multilinear operators on CðK;GÞ and ðp; p1; . . .; pnÞdominated
multilinear operators in the sense of Dinculeanu on CðK;GÞ, where K is a
compact Hausdorff space and G a Banach space. We also treat the connection
between an operator T and its associated operators Tt; T~ and T# for certain classes
Description
Keywords
Dominated multilinear operators (p, G)-summing operators ð~ p;GÞ-summing operators Pietsch domination–factorization theorem