# Toeplitz matrices and convergence

Fundamenta Mathematicae (2000)

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

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topMildenberger, 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 -

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