A note on the Mackey-star topology on a dual Banach space

[EN] By using a result in Kirk (Pac J Math 45:543 554, 1973), we show that there are separable Banach spaces such that their dual spaces, endowed with the Mackey-star topology, are not analytic. This solves a question raised in Kakol et al. (Descriptive topology in selected topics of functional analysis, Springer, 2011), and in Kakol and López-Pellicer (RACSAM 105:39 70, 2011).A. J. Guirao is Supported in part by MICINN and FEDER (Project MTM2008-05396), by Fundación Séneca (Project 08848/PI/08), by Generalitat Valenciana (GV/2010/036), and by Universitat Politècnica de València (project PAID-06-09-2829). V. Montesinos is Supported in part by Project MICINN MTM2011-22417, Generalitat Valenciana (GV/2010/036), and by Universitat Politècnica de València (Project PAID-06-09-2829).Guirao Sánchez, AJ.; Montesinos Santalucia, V. (2015). A note on the Mackey-star topology on a dual Banach space. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 109(2):417-418. https://doi.org/10.1007/s13398-014-0192-44174181092Fabian, M., Montesinos, V., Zizler, V.: On weak compactness in $$L_1$$ L 1 spaces. Rocky Mt. J. Math. 39, 1885–1893 (2009)Grothendieck, A.: Topological vector spaces, Translated from the French by Orlando Chaljub. Gordon and Breach Science publishers, New York (1973)Kąkol, J., López-Pellicer, M.: On realcompact topological vector spaces. RACSAM 105, 39–70 (2011)Kąkol, J., Kubiś, W., López-Pellicer, M.: Descriptive Topology in Selected Topics of Functional Analysis. In: Developments in Mathematics, vol. 24. Springer, New York (2011)Kirk, R.B.: A note on the Mackey topology for $$(C^b(X)^*, C^b(X))$$ ( C b ( X ) ∗ , C b ( X ) ) . Pac. J. Math. 45(2), 543–554 (1973)Köthe, G.: Topological vector spaces I, Translated by D.J.H. Garling, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Band 159, 2nd edn. Springer, New York (1969)Schlüchtermann, G., Wheeler, R.F.: On strongly WCG Banach spaces. Math. Z. 199, 387–398 (1988