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Some remarks on *-Baire-like and b-*-Baire-like spaces. (English) Zbl 0615.46001
An extension of the Banach-Mackey theorem is used to obtain the *-Baire- likeness of spaces lying between the product space $$E=\prod E_ s$$ and the direct sum $$\oplus E_ s$$, endowed with the product topology. The open mapping theorem for *-Baire-like spaces and the theorem of bilinear mappings are also obtained.
##### MSC:
 46A08 Barrelled spaces, bornological spaces 46A30 Open mapping and closed graph theorems; completeness (including $$B$$-, $$B_r$$-completeness) 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than $$\mathbb{R}$$, etc.)
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##### References:
 [1] ADASCH N., ERNST B., KEIM D.: Topological vector spaces. Lecture Notes in Math. 639, Berlin 1978. · Zbl 0397.46005 [2] BOURBAKI N.: Éléments de Mathématique. Topologie Générale. Chap. 9, Paris 1974. · Zbl 1107.54002 [3] EBERHARDT V.: Über einen Graphensatz fur Abbildungen mit normiertem Zielraum. Manuscripta Math., 12, 1974, 47-65. · Zbl 0275.46002 [4] HORVATH J.: Topological vector spaces and distributions. Addison-Wesley Publishing Company, 1966. · Zbl 0143.15101 [5] KAKOL J.: Topological linear spaces with some Baire-like properties. Functiones et Approximatio, 13, 1982, 109-116. · Zbl 0512.46001 [6] KAKOL J.: Some remarks on subspaces and products of ultrabornological spaces. Simon Stevin, 57, 1983, 83-97. · Zbl 0523.46001 [7] KÖTHE G.: Die Bildräume abgeschlossener Operatoren. J. reine engew. Math., 232, 1968, 110-111. · Zbl 0157.21003 [8] TODD A. R.: Covering of products of linear topological spaces. J. Austral. Math. Soc., 29, 1980, 281-290. · Zbl 0436.46003
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