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Norm attainment for multilinear operators and polynomials on Banach Spaces and Banach lattices
Luis A. Garcia, José Lucas P. Luiz, Vinícius C. C. Miranda
We study norm attainment for multilinear operators and homogeneous polynomials between Banach spaces, as well as for positive multilinear operators between Banach lattices. We esta…
Arens extensions of disjointness preserving multilinear operators
Geraldo Botelho, Luis Alberto Garcia, Vinícius C. C. Miranda
First we give a counterexample showing that, unlike the second adjoint of a disjointness preserving linear operator, Arens extensions of disjointness preserving multilinear operato…
Disjoint -convergent operators and their adjoints
Geraldo Botelho, Luis Alberto Garcia, Vinícius C. C. Miranda
First we give conditions on a Banach lattice so that an operator from to any Banach space is disjoint -convergent if and only if is almost Dunford-Pettis. Then w…
Aron-Berner extensions of almost Dunford-Pettis multilinear operators
Geraldo Botelho, Luis Alberto Garcia
We prove several results establishing conditions on the Banach lattices E_1,..., E_m and F so that the Aron-Berner extensions of (separately) almost Dunford-Pettis m-linear operato…
Operators whose adjoints and second adjoints are almost Dunford-Pettis
Geraldo Botelho, Luis Alberto Garcia
First we characterize the Banach lattices E whose biduals have the positive Schur property by means of second adjoints of operators on E being almost Dunford-Pettis. Next we extend…
Order continuity of Arens extensions of regular multilinear operators
Geraldo Botelho, Luis Alberto Garcia
First we give a counterexample showing that recent results on separate order continuity of Arens extensions of multilinear operators cannot be improved to get separate order contin…
Bidual extensions of Riesz multimorphisms
Geraldo Botelho, Luis Alberto Garcia
We prove that all Arens extensions of finite rank Riesz multimorphisms taking values in Archimedean Riesz spaces coincide and are Riesz multimorphisms. Partial results for arbitrar…