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On the structure of G-spaces

100%

Castillo J. M. F.

Colloquium Mathematicum

1991

tom 62

nr 1

81-90

Banach spaces in which all multilinear forms are weakly sequentially continuous

51%

Castillo J. M. F., García R., Gonzalo R.

Studia Mathematica

1999

tom 136

nr 2

121-145

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].

Ograniczanie wyników

1 Colloquium Mathematicum

1 Studia Mathematica

2 Castillo J. M. F.

1 García R.

1 Gonzalo R.

1 1999

1 1991

Wyniki wyszukiwania

On the structure of G-spaces

Banach spaces in which all multilinear forms are weakly sequentially continuous