Toeplitz matrices and convergence
Mildenberger, Heike
Fundamenta Mathematicae, Tome 163 (2000), p. 175-189 / Harvested from The Polish Digital Mathematics Library
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We investigate ||χ𝔸,2||, the minimum cardinality of a subset of 2ω that cannot be made convergent by multiplication with a single matrix taken from 𝔸, for different sets 𝔸 of Toeplitz matrices, and show that for some sets 𝔸 it coincides with the splitting number. We show that there is no Galois-Tukey connection from the chaos relation on the diagonal matrices to the chaos relation on the Toeplitz matrices with the identity on 2ω as first component. With Suslin c.c.c. forcing we show that ||χ𝕄,2|| < ∙ is consistent relative to ZFC.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:212464 
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Mildenberger, Heike. Toeplitz matrices and convergence. Fundamenta Mathematicae, Tome 163 (2000) pp. 175-189. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv165i2p175bwm/

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