SciELO - Scientific Electronic Library Online

vol.20 número2TOPOLOGIES POLAIRES COMPATIBLES AVEC UNE DUALITÉ SÉPARANTE SUR UN CORPS VALUÉ NON-ARCHIMÉDIEN índice de autoresíndice de materiabúsqueda de artículos
Home Pagelista alfabética de revistas  

Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.20 n.2 Antofagasta ago. 2001 



New Mexico State University - U. S. A.



We consider the Banach-Mackey property for pairs of vector spaces E and E' which are in duality. Let A be an algebra of sets and assume that P is an additive map from A into the projection operators on E. We define a continuous gliding hump property for the map P and show that pairs with this gliding hump property and anoter measure theoretic property are Banach-Mackey pairs, i. e., weakly bounded subsets of E are strongly bounded. Examples of vector valued function spaces, such as the space of Pettis integrable functions, which satisfy these conditions are given.




[B] S. Banach, Oeuvres II, PWN, Warsaw, (1979).        [ Links ]

[BF] J. Boos and D. Fleming, Gliding Hump Properties and Some Aplications, Int. J. Math. Math. Sci., 18, pp. 121-132, (1995).        [ Links ]

[DFP] S. Díaz, M. Florencio and P. Paúl, A uniform boundedness theorem for for L¥ (m,E ), Arch. Math.(Basel), 60, pp. 73-78, (1993).        [ Links ]

[DFFP1] S. Díaz, A. Fernández, M. Florencio and P. Paúl, An abstract Banach-Steinhaus theorem and aplications to function spaces, Resultate Math., 23, pp. 242-250, (1993).        [ Links ]

[DFFP2] S. Díaz, A. Fernández, M. Florencio and P. Paúl, A Wide Class of Ultrabornological Spaces of Measurable Functions, J. Math. Anal. Appl., 190, pp. 697-713 (1995).        [ Links ]

[Du] J. Diestel and J.J. Uhl, Vector Measures, Amer. Math. Soc., Surveys # 15, Providence, (1977).        [ Links ]

[Do] I. Dobrakov, On Integration in Banach Spaces I, Czech. Math. J., 20, pp. 511-536, (1970).        [ Links ]

[DFP1] L. Drewnowski, M Florencio, and P. Paúl, The Space of Pettis Integrable Functions is Barrelled, Proc. Amer. Math. Soc., 114, pp. 341-351, (1992).        [ Links ]

[DFP2] L. Drewnowski, M Florencio, and P. Paúl, Uniform boundedness of operators and barrelledness in spaces with Boolean algebras of projections. Atti. Sem. Mat. Fis., Univ. Modena XLI, pp. 317-329, (1993).        [ Links ]

[DS] N. Dunford and J. Schwartz, Linear Operators I, Interscience, N. Y., (1958).        [ Links ]

[FMP] M. Florencio, F Mayoral and P. Paúl, Diedonné-Köthe Duality for Vector-Valued Function Spaces, Quaest. Math., 20, pp. 185-214, (1997).         [ Links ]

[FM] D. Fremlin and J. Mendoza, On the Integration of Vector-Valued Functions, Illinois J. Math., 38, pp. 127-147, (1994).        [ Links ]

[G] R. Gordan, The McShane Integral of Banach-Valued Functions, Illinois J. Math., 34, pp. 557-567, (1990).        [ Links ]

[Ha] H. Hahn. Über Folgen linearen Operationen, Monatsch. für Math. und Phys., 32, pp. 1-88 (1922).        [ Links ]

[HT] E. Hellinger and O. Toeplitz, Gründlagen für eine Theorie den unendlichen Matrizen, Math. Ann., 69, pp. 289-330, (1910).        [ Links ]

[Hi] T.H. Hilldebrandt, On Uniform Limitedness of Sets of Functional Operations, Bull. Amer. Math. Soc., 29, pp. 309-315, (1923).        [ Links ]

[L] H. Lebesgue, Sur les intégrales singuliéres, Ann. de Toulouse, 1, pp. 25-117, (1909).        [ Links ]

[RR] K. P. S. Rao, and M. Rao, Theory of Charges, Academic Press, N. Y., (1983).        [ Links ]

[Sch] J. Schur, Über lineare Transformation in der Theorie die unendlichen Reihen, J Reine Angew Math., 151, pp. 79-111, (1920).        [ Links ]

[Sw1] C. Swartz, An Introduction to Functional Analysis. Marcel Dekker, N. Y., (1992).        [ Links ]

[Sw2] C. Swartz, Measure, Integration and Functional Spaces, World Sci. Publ., Singapore, (1994).        [ Links ]

[Sw3] C. Swartz, Infinite Matrices and the Gliding Hump, World Sci. Publ., Singapore, (1996).        [ Links ]

[Sw4] C. Swartz, Beppo Levi's Theorem for the Vector-Valued McShane Integral and Aplications, Bull.Belgian Math. Soc., 4, pp. 589-599, (1997).        [ Links ]

[Sw5] C. Swartz, Topological Properties of the Space of Integrable Functions with respect to a Charge, Ricerche di Mat., to appear.        [ Links ]

[Sz] P. Szeptycki, Notes on integral transformations, Diss. Math., 231, (1984).        [ Links ]

[Wi] A. Wilansky. Modern Methods in Topological Vector Spaces, McGraw-Hill, N. Y., (1978).        [ Links ]


Received : December, 2000.

Charles Swartz

Department of Mathematical Sciences

New Mexico State University

Las Cruces, NM 88003



Creative Commons License Todo el contenido de esta revista, excepto dónde está identificado, está bajo una Licencia Creative Commons