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A bilinear version of Orlicz-Pettis theorem |
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| Authors: | O Blasco JM Calabuig T Signes |
| Institution: | a Department of Mathematics, Universitat de València, Burjassot 46100, València, Spain b Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, València 46022, Spain c Department of Applied Mathematics, Universidad de Murcia, Espinardo 30100, Murcia, Spain |
| Abstract: | Given three Banach spaces X, Y and Z and a bounded bilinear map  , a sequence x=n(xn)⊆X is called B-absolutely summable if  is finite for any y∈Y. Connections of this space with  are presented. A sequence x=n(xn)⊆X is called B-unconditionally summable if  is finite for any y∈Y and z∗∈Z∗ and for any M⊆N there exists xM∈X for which ∑n∈M〈B(xn,y),z∗〉=〈B(xM,y),z∗〉 for all y∈Y and z∗∈Z∗. A bilinear version of Orlicz-Pettis theorem is given in this setting and some applications are presented. |
| Keywords: | Absolute and strong summability Sequence spaces Banach sequence spaces |
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