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On a Question Posed by D. Leviatan and L. Lorch

Published online by Cambridge University Press:  20 November 2018

Jean Tzimbalario
Jean Tzimbalario*
Affiliation:
Tel Aviv University, Tel Aviv, Israel
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In this note we construct a pair of regular matrices T1 and T2 such that T1 is stronger than T2, and the T2-transforms of all bounded sequences are such that the sets of limit-points are connected, while there is a bounded sequence such that the set of limit-points of its T1-transform is not connected. This provides a negative answer to a question posed by Leviatan and Lorch [3, §6, (c)].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 3 , September 1972 , pp. 453
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Barone, H. G., Limit points of sequences and their transforms by methods of summability, Duke Math. J. 5 (1939), 740-752.Google Scholar
2. Erdös, P. and Piranian, G., Laconicity and redundancy of Toeplitz-matrices, Math. Z. 83 (1964), 381-394.Google Scholar
3. Leviatan, D. and Lorch, L., On the connectedness of the limit-points of certain transforms of bounded sequences, Canad. Math. Bull. (2) 14 (1971), 175-181.Google Scholar