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See detailOn a group theoretic generalization of the Morse-Hedlund theorem
Charlier, Emilie ULg; Puzynina, Svetlana; Zamboni, Luca

in Proceedings of the American Mathematical Society (2017), 145(8), 33813394

In their 1938 seminal paper on symbolic dynamics, Morse and Hedlund proved that every aperiodic infinite word contains at least n+ 1 distinct factors of each length n. They further showed that an infinite ... [more ▼]

In their 1938 seminal paper on symbolic dynamics, Morse and Hedlund proved that every aperiodic infinite word contains at least n+ 1 distinct factors of each length n. They further showed that an infinite word has exactly n+ 1 distinct factors of each length n if and only if it is binary, aperiodic and balanced, i.e., it is a Sturmian word. In this paper we obtain a broad generalization of the Morse-Hedlund theorem via group actions. [less ▲]

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See detailLOCALLY BOUNDED NONCONTINUOUS LINEAR-FORMS ON STRONG DUALS OF NONDISTINGUISHED KOTHE ECHELON SPACES
Bastin, Françoise ULg; Bonet, Jose

in Proceedings of the American Mathematical Society (1990), 108(3), 769-774

In this note it is proved that if Al (A) is any nondistinguished Kothe echelon space of order one and K. ,0 (AI (A))' is its strong dual, then there is even a linear form : K - C which is locally bounded ... [more ▼]

In this note it is proved that if Al (A) is any nondistinguished Kothe echelon space of order one and K. ,0 (AI (A))' is its strong dual, then there is even a linear form : K - C which is locally bounded (i.e. bounded on the bounded sets) but not continuous. It is also shown that every nondistinguished Kothe echelon space contains a sectional subspace with a particular structure [less ▲]

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