Toeplitz matrices and convergence

Heike Mildenberger

Fundamenta Mathematicae (2000)

  • Volume: 165, Issue: 2, page 175-189
  • ISSN: 0016-2736

Abstract

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We investigate | | χ 𝔸 , 2 | | , the minimum cardinality of a subset of 2 ω 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 2 ω as first component. With Suslin c.c.c. forcing we show that | | χ 𝕄 , 2 | | < ∙ is consistent relative to ZFC.

How to cite

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Mildenberger, Heike. "Toeplitz matrices and convergence." Fundamenta Mathematicae 165.2 (2000): 175-189. <http://eudml.org/doc/212464>.

@article{Mildenberger2000,
abstract = {We investigate $||χ_\mathbb \{A\},2||$, the minimum cardinality of a subset of $2^ω$ that cannot be made convergent by multiplication with a single matrix taken from $\mathbb \{A\}$, for different sets $\mathbb \{A\}$ of Toeplitz matrices, and show that for some sets $\mathbb \{A\}$ 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 $2^ω$ as first component. With Suslin c.c.c. forcing we show that $||χ_\mathbb \{M\},2||$ < $∙ $ is consistent relative to ZFC.},
author = {Mildenberger, Heike},
journal = {Fundamenta Mathematicae},
keywords = {Toeplitz matrices; splitting number; Galois-Tukey connection; chaos relation; Suslin c.c.c. forcing; consistency; convergence},
language = {eng},
number = {2},
pages = {175-189},
title = {Toeplitz matrices and convergence},
url = {http://eudml.org/doc/212464},
volume = {165},
year = {2000},
}

TY - JOUR
AU - Mildenberger, Heike
TI - Toeplitz matrices and convergence
JO - Fundamenta Mathematicae
PY - 2000
VL - 165
IS - 2
SP - 175
EP - 189
AB - We investigate $||χ_\mathbb {A},2||$, the minimum cardinality of a subset of $2^ω$ that cannot be made convergent by multiplication with a single matrix taken from $\mathbb {A}$, for different sets $\mathbb {A}$ of Toeplitz matrices, and show that for some sets $\mathbb {A}$ 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 $2^ω$ as first component. With Suslin c.c.c. forcing we show that $||χ_\mathbb {M},2||$ < $∙ $ is consistent relative to ZFC.
LA - eng
KW - Toeplitz matrices; splitting number; Galois-Tukey connection; chaos relation; Suslin c.c.c. forcing; consistency; convergence
UR - http://eudml.org/doc/212464
ER -

References

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