caa a22 4500 388046600 CHVBK 20180307125040.0 cr unu---uuuuu 161130e199810 xx s 000 0 eng 10.1017/S1446788700034947 doi S1446788700034947 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700034947 Operators and the space of integrable scalar functions with respect to a Fréchet-valued measure [Elektronische Daten] We consider the space L1 (ν, X) of all real functions that are integrable with respect to a measure v with values in a real Fréchet space X. We study L-weak compactness in this space. We consider the problem of the relationship between the existence of copies of l∞ in the space of all linear continuous operators from a complete DF-space Y to a Fréchet lattice E with the Lebesgue property and the coincidence of this space with some ideal of compact operators. We give sufficient conditions on the measure ν and the space X that imply that L1 (ν, X) has the Dunford-Pettis property. Applications of these results to Fréchet AL-spaces and Köthe sequence spaces are also given. Copyright © Australian Mathematical Society 1998 primary 46A04 nationallicence 46A40 nationallicence 46G10 nationallicence 47B07 nationallicence Fréchet lattice nationallicence L-weak compactness nationallicence Dunford-Pettis property nationallicence L-weakly compact operators nationallicence generalized AL-spaces nationallicence Köthe sequences spaces nationallicence Fernández Antonio Department Matemática Aplicada II, Escuela Superior de Ingenieros, Camino de los Descubrimientos, s/n 41092-Sevilla, Spain e-mail: anfercar@matinc.us.es Naranjo Francisco Department Matemática Aplicada II, Escuela Superior de Ingenieros, Camino de los Descubrimientos, s/n 41092-Sevilla, Spain e-mail: anfercar@matinc.us.es Journal of the Australian Mathematical Society Cambridge University Press 65/2(1998-10), 176-193 1446-7887 65:2<176 1998 65 JAZ https://doi.org/10.1017/S1446788700034947 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700034947 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Fernández Antonio Department Matemática Aplicada II, Escuela Superior de Ingenieros, Camino de los Descubrimientos, s/n 41092-Sevilla, Spain e-mail: anfercar@matinc.us.es NATIONALLICENCE 700 1- Naranjo Francisco Department Matemática Aplicada II, Escuela Superior de Ingenieros, Camino de los Descubrimientos, s/n 41092-Sevilla, Spain e-mail: anfercar@matinc.us.es NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 65/2(1998-10), 176-193 1446-7887 65:2<176 1998 65 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge