Positive p-summing operators and disjoint p-summing operators

Chen, Dongyang; Belacel, Amar; Chávez-Domínguez, Javier Alejandro

doi:10.1007/s11117-020-00798-y

Cited by 4 publications

(9 citation statements)

References 11 publications

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“…In [6], we prove the following duality relationships between positive p-summing operators and positive p-majorizing operators which will be used later.…”

Section: Positively P-nuclear Operatorsmentioning

confidence: 97%

“…To describe the conjugate of the space of positively p-nuclear operators, we need the concept of positive p-majorizing operators introduced in [6].…”

Section: Positively P-nuclear Operatorsmentioning

confidence: 99%

“…Definition 2.5. [6] We say that an operator S : E → X is positive p-majorizing if there exists a constant C > 0 such…”

Section: Positively P-nuclear Operatorsmentioning

confidence: 99%

“…This paper is a continuous work of [6]. The aim of the present paper is to develop the theory of p-nuclear and p-integral operators in the Banach lattice setting.…”

Section: Introductionmentioning

confidence: 99%

“…Secondly, we establish a representation theorem for ( N p (X, E)) * , the dual space of the positively p-nuclear operators, by means of positive p-majorizing operators introduced by D. Chen, A. Belacel and J. A. Chávez-Domínguez [6] if E has the approximation property or X * has the positive metric approximation property. Recall that when E * has the approximation property, any operator T : E → F with nuclear adjoint is nuclear and both nuclear norms coincide (see for instance [31,Proposition 4.10]).…”

Section: Introductionmentioning

confidence: 99%

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Positively $p$-nuclear operators, positively $p$-integral operators and approximation properties

Chen¹,

Belacel²,

Chávez-Domínguez³

2021

Preprint

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In the present paper, we introduce and investigate a new class of positively p-nuclear operators that are positive analogues of right p-nuclear operators. One of our main results establishes an identification of the dual space of positively p-nuclear operators with the class of positive p-majorizing operators that is a dual notion of positive p-summing operators. As applications, we prove the duality relationships between latticially p-nuclear operators introduced by O. I. Zhukova and positively p-nuclear operators. We also introduce a new concept of positively pintegral operators via positively p-nuclear operators and prove that the inclusion map from L p * (µ) to L 1 (µ)(µ finite) is positively p-integral. New characterizations of latticially p-integral operators by O. I. Zhukova and positively p-integral operators are presented and used to prove that an operator is latticially p-integral (resp. positively p-integral) precisely when its second adjoint is. Finally, we describe the space of positively p * -integral operators as the dual of the • Υp -closure of the subspace of finite rank operators in the space of positive p-majorizing operators. Approximation properties, even positive approximation properties, are needed in establishing main identifications.

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“…In [6], we prove the following duality relationships between positive p-summing operators and positive p-majorizing operators which will be used later.…”

Section: Positively P-nuclear Operatorsmentioning

confidence: 97%

“…To describe the conjugate of the space of positively p-nuclear operators, we need the concept of positive p-majorizing operators introduced in [6].…”

Section: Positively P-nuclear Operatorsmentioning

confidence: 99%

“…Definition 2.5. [6] We say that an operator S : E → X is positive p-majorizing if there exists a constant C > 0 such…”

Section: Positively P-nuclear Operatorsmentioning

confidence: 99%

“…This paper is a continuous work of [6]. The aim of the present paper is to develop the theory of p-nuclear and p-integral operators in the Banach lattice setting.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations