Some remarks on *-Baire-like and b-*-Baire-like spaces. (English) Zbl 0615.46001

Kąkol, Jerzy

Math. Slovaca 36, 233-239 (1986).

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.)

Keywords:

Banach-Mackey theorem; *-Baire-likeness; product space; direct sum; open mapping theorem; theorem of bilinear mappings

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