The Null Ideal of a Matrix: 11083

2006 ◽  
Vol 113 (4) ◽  
pp. 371
Author(s):  
William P. Wardlaw ◽  
Jean-Pierre Grivaux
Keyword(s):  
Null Ideal

scholarly journals Keeping additivity of the null ideal small

1997 ◽  
Vol 125 (8) ◽  
pp. 2443-2451 ◽  
Author(s):  
Jindřich Zapletal
Keyword(s):  
Null Ideal

scholarly journals Hechler’s theorem for the null ideal

2004 ◽  
Vol 43 (5) ◽  
pp. 703-722 ◽  
Author(s):  
Maxim R. Burke ◽  
Masaru Kada
Keyword(s):  
Null Ideal

scholarly journals REPRESENTATIONS OF IDEALS IN POLISH GROUPS AND IN BANACH SPACES

2015 ◽  
Vol 80 (4) ◽  
pp. 1268-1289 ◽  
Author(s):  
PIOTR BORODULIN–NADZIEJA ◽  
BARNABÁS FARKAS ◽  
GRZEGORZ PLEBANEK
Keyword(s):  
Banach Space ◽  
Abelian Group ◽  
Banach Spaces ◽  
Open Problems ◽  
Polish Groups ◽  
Polish Group ◽  
Focus On The Family ◽  
The Family ◽  
Null Ideal ◽  
Defining Sequence

AbstractWe investigate ideals of the form {A⊆ω: Σn∈Axnis unconditionally convergent} where (xn)n∈ωis a sequence in a Polish group or in a Banach space. If an ideal onωcan be seen in this form for some sequence inX, then we say that it is representable inX.After numerous examples we show the following theorems: (1) An ideal is representable in a Polish Abelian group iff it is an analytic P-ideal. (2) An ideal is representable in a Banach space iff it is a nonpathological analytic P-ideal.We focus on the family of ideals representable inc0. We characterize this property via the defining sequence of measures. We prove that the trace of the null ideal, Farah’s ideal, and Tsirelson ideals are not representable inc0, and that a tallFσP-ideal is representable inc0iff it is a summable ideal. Also, we provide an example of a peculiar ideal which is representable inℓ1but not in ℝ.Finally, we summarize some open problems of this topic.

On possible restrictions of the null ideal

2019 ◽  
Vol 19 (02) ◽  
pp. 1950008
Author(s):  
Ashutosh Kumar ◽  
Saharon Shelah
Keyword(s):  
Null Ideal ◽  
Null Set

We prove that the null ideal restricted to a non-null set of reals could be isomorphic to a variety of sigma ideals. Using this, we show that the following are consistent: (1) There is a non-null subset of plane each of whose non-null subsets contains three collinear points. (2) There is a partition of a non-null set of reals into null sets, each of size [Formula: see text], such that every transversal of this partition is null.

scholarly journals Polynomial functions on subsets of non-commutative rings — a link between ringsets and null-ideal sets

2018 ◽  
Vol 20 ◽  
pp. 01003
Author(s):  
Sophie Frisch
Keyword(s):  
Commutative Ring ◽  
Commutative Rings ◽  
The Other ◽  
Polynomial Functions ◽  
Other Hand ◽  
Null Ideal

Regarding polynomial functions on a subset S of a non-commutative ring R, that is, functions induced by polynomials in R[x] (whose variable commutes with the coeffcients), we show connections between, on one hand, sets S such that the integer-valued polynomials on S form a ring, and, on the other hand, sets S such that the set of polynomials in R[x] that are zero on S is an ideal of R[x].

Keeping the covering number of the null ideal small

2015 ◽  
Vol 231 (2) ◽  
pp. 139-159
Author(s):  
Teruyuki Yorioka
Keyword(s):  
Covering Number ◽  
Null Ideal

No Tukey reduction of Lebesgue null to Silver null sets

2018 ◽  
Vol 18 (02) ◽  
pp. 1850011
Author(s):  
Otmar Spinas
Keyword(s):  
Recent Result ◽  
Null Ideal ◽  
Meager Ideal

We prove that consistently the Lebesgue null ideal is not Tukey reducible to the Silver null ideal. This contrasts with the situation for the meager ideal which, by a recent result of the author, Spinas [Silver trees and Cohen reals, Israel J. Math. 211 (2016) 473–480] is Tukey reducible to the Silver ideal.

scholarly journals A null ideal for inaccessibles

2017 ◽  
Vol 56 (5-6) ◽  
pp. 691-697 ◽  
Author(s):  
Sy-David Friedman ◽  
Giorgio Laguzzi
Keyword(s):  
Null Ideal
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