Wyniki wyszukiwania

1

Banach spaces in which all multilinear forms are weakly sequentially continuous

100%

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

Studia Mathematica

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1999

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tom 136

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nr 2

121-145

EN

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].

2

Existence theorem for the Hammerstein integral equation

100%

Cichoń M., Kubiaczyk I.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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1996

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tom 16

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nr 2

171-177

EN

In this paper we prove an existence theorem for the Hammerstein integral equation $x(t) = p(t) + λ ∫_I K(t,s)f(s,x(s))ds$, where the integral is taken in the sense of Pettis. In this theorem continuity assumptions for f are replaced by weak sequential continuity and the compactness condition is expressed in terms of the measures of weak noncompactness. Our equation is considered in general Banach spaces.

3

Strong continuity of semigroup homomorphisms

88%

Basit B., Pryde A.

Studia Mathematica

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1999

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tom 132

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nr 1

71-78

EN

Let J be an abelian topological semigroup and C a subset of a Banach space X. Let L(X) be the space of bounded linear operators on X and Lip(C) the space of Lipschitz functions ⨍: C → C. We exhibit a large class of semigroups J for which every weakly continuous semigroup homomorphism T: J → L(X) is necessarily strongly continuous. Similar results are obtained for weakly continuous homomorphisms T: J → Lip(C) and for strongly measurable homomorphisms T: J → L(X).

Ograniczanie wyników

2 Studia Mathematica

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Basit B.

1 Castillo J. M. F.

1 Cichoń M.

1 García R.

1 Gonzalo R.

1 Kubiaczyk I.

1 Pryde A.

2 1999

1 1996

Banach spaces in which all multilinear forms are weakly sequentially continuous

Existence theorem for the Hammerstein integral equation

Strong continuity of semigroup homomorphisms