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2000 | 165 | 2 | 175-189
Tytuł artykułu

Toeplitz matrices and convergence

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Języki publikacji
EN
Abstrakty
EN
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 $||χ_\mathbb M,2||$ < $\gb ∙ \gs$ is consistent relative to ZFC.
Słowa kluczowe
Rocznik
Tom
165
Numer
2
Strony
175-189
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-07-05
poprawiono
2000-02-27
Twórcy
  • Institute of Mathematics, Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel, heike@math.huji.ac.il
Bibliografia
  • [1] T. Bartoszyński and H. Judah, Set Theory. On the Structure of the Real Line, A. K. Peters, Wellesley, MA, 1995.
  • [2] H. Bauer, Probability Theory, de Gruyter, 4th ed., 1996.
  • [3] A. Blass, Cardinal characteristics and the product of countably many infinite cyclic groups, J. Algebra 169 (1995), 512-540.
  • [4] A. Blass, Reductions between cardinal characteristics of the continuum, in: T. Bartoszyński and M. Scheepers (eds.), Set Theory (Boise 1992-94), Contemp. Math. 192, Amer. Math. Soc., 1996, 31-49.
  • [5] A. Blass, Combinatorial cardinal characteristics of the continuum, in: M. Foreman, A. Kanamori, and M. Magidor (eds.), Handbook of Set Theory, Kluwer, to appear.
  • [6] R. Cooke, Infinite Matrices and Sequence Spaces, MacMillan, 1950.
  • [7] E. van Douwen, The integers and topology, in: K. Kunen and J. Vaughan (eds.), Handbook of Set-Theoretic Topology, North-Holland, 1984, 111-167.
  • [8] A. Dow, Tree π-bases for $β\mathbb N - \mathbb N$, Topology Appl. 33 (1989), 3-19.
  • [9] T. Jech, Set Theory, Addison-Wesley, 1978.
  • [10] H. Judah and S. Shelah, Suslin forcing, J. Symbolic Logic 53 (1988), 1188-1207.
  • [11] A. Kamburelis and B. Węglorz, Splittings, Arch. Math. Logic 35 (1996), 263-277.
  • [12] S. Shelah, Proper Forcing, Lecture Notes in Math. 940, Springer, 1982.
  • [13] J. E.Vaughan, Small uncountable cardinals and topology, in: J. van Mill and G. Reed (eds.), Open Problems in Topology, Elsevier, 1990, 195-218.
  • [14] P. Vojtáš, Set theoretic characteristics of summability and convergence of series, Comment. Math. Univ. Carolin. 28 (1987), 173-184.
  • [15] P. Vojtáš, More on set theoretic characteristics of summability by regular (Toeplitz) matrices, Comment. Math. Univ. Carolin. 29 (1988), 97-102.
  • [16] P. Vojtáš, Series and Toeplitz matrices (a global implicit approach), Tatra Mt. Math. J., to appear.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv165i2p175bwm
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