Publications de l’Institut Mathématique, Nouvelle SérieVol. 101[115], pp. 151–160 (2017)
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Publications de l’Institut Mathématique, Nouvelle Série Vol. 101[115], pp. 151–160 (2017) |
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ON THE MIKUSIŃSKI–ANTOSIK DIAGONAL THEOREM AND THE EQUIVALENCE OF TWO TYPES OF CONVERGENCE IN KÖTHE SPACESAndrzej Kamiński, Sławomir SorekFaculty of Mathematics and Natural Sciences, University of Rzeszów, Rzeszów, PolandAbstract: We present a simple proof of the Mikusiński–Antosik diagonal theorem and apply this result to prove, in an extended form, the theorem on the equivalence of the strong and weak boundedness of sets and, consequently, of the strong and weak convergence of sequences in Köthe spaces. Keywords: quasi-normed group; sliding-hump technique; diagonal theorems; Köthe spaces; boundedness and convergence in Köthe spaces Classification (MSC2000): 15A45, 40H05; 46A03 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 24 Apr 2017. This page was last modified: 11 May 2017.
© 2017 Mathematical Institute of the Serbian Academy of Science and Arts
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