- Tytuł:
- Banach spaces in which all multilinear forms are weakly sequentially continuous
- Autorzy:
-
Castillo, Jesús M.F.
García, Ricardo
Gonzalo, Raquel - Tematy:
-
multilinear forms
polynomials
weak continuity - Pokaż więcej
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Powiązania:
- https://bibliotekanauki.pl/articles/1216281.pdf Link otwiera się w nowym oknie
- Opis:
- We solve several problems in the theory of polynomials in Banach spaces. (i) There exist Banach spaces without the Dunford-Pettis property and without upper p-estimates in which all multilinear forms are weakly sequentially continuous: some Lorentz sequence spaces, their natural preduals and, most notably, the dual of Schreier's space. (ii) There exist Banach spaces X without the Dunford-Pettis property such that all multilinear forms on X and X* are weakly sequentially continuous; this gives an answer to a question of Dimant and Zalduendo [20]. (iii) The sum of two polynomially null sequences need not be polynomially null; this answers a question of Biström, Jaramillo and Lindström [8] and also of González and Gutiérrez [23]. (iv), (v) The absolutely convex closed hull of a pw-compact set need not be pw-compact; the projective tensor product of two polynomially null sequences need not be a polynomially null sequence. This answers two questions of González and Gutiérrez [23]. (vi) There exists a Banach space without property (P); this answers a question of Aron, Choi and Llavona [5].
- Dostawca treści:
- Biblioteka Nauki
Artykuł