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Nuclear and GP-Nuclear Groups |
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| Authors: | X. Domínguez V. Tarieladze |
| Affiliation: | (1) Departamento de Métodos Matemáticos y de Representación E.T.S.I. Caminos, Canales y Puertos, Universidad de a Coruña Campus de Elviña, a Coruña, Spain E-mail;(2) Muskhelishvili Institute of Computational Mathematics Georgian Academy of Sciences, Tbilisi-, 93, Georgia E-mail |
| Abstract: | We define GP-nuclear groups as topological Abelian groups for which the groups of summable and absolutely summable sequences are the same algebraically and topologically. It is shown that in the metrizable case only the algebraic coincidence of the mentioned groups is needed for GP-nuclearity. Some permanence properties of the class of GP-nuclear groups are obtained. Our final result asserts that nuclear groups in the sense of Banaszczyk are GP-nuclear. The validity of the converse assertion remains open. |
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