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Dichotomy theorems for random matrices and closed ideals of operators on (\bigoplus_{n=1}^\infty\ell_1^n)_{c_0}.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Dichotomy theorems for random matrices and closed ideals of operators on (\bigoplus_{n=1}^\infty\ell_1^n)_{c_0}. / Laustsen, Niels Jakob; Odell, Edward; Schlumprecht, Thomas et al.
In: Journal of the London Mathematical Society, Vol. 86, No. 1, 08.2012, p. 235-258.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Laustsen, NJ, Odell, E, Schlumprecht, T & Zsak, A 2012, 'Dichotomy theorems for random matrices and closed ideals of operators on (\bigoplus_{n=1}^\infty\ell_1^n)_{c_0}.', Journal of the London Mathematical Society, vol. 86, no. 1, pp. 235-258. https://doi.org/10.1112/jlms/jdr083

APA

Laustsen, N. J., Odell, E., Schlumprecht, T., & Zsak, A. (2012). Dichotomy theorems for random matrices and closed ideals of operators on (\bigoplus_{n=1}^\infty\ell_1^n)_{c_0}. Journal of the London Mathematical Society, 86(1), 235-258. https://doi.org/10.1112/jlms/jdr083

Vancouver

Laustsen NJ, Odell E, Schlumprecht T, Zsak A. Dichotomy theorems for random matrices and closed ideals of operators on (\bigoplus_{n=1}^\infty\ell_1^n)_{c_0}. Journal of the London Mathematical Society. 2012 Aug;86(1):235-258. doi: 10.1112/jlms/jdr083

Author

Laustsen, Niels Jakob ; Odell, Edward ; Schlumprecht, Thomas et al. / Dichotomy theorems for random matrices and closed ideals of operators on (\bigoplus_{n=1}^\infty\ell_1^n)_{c_0}. In: Journal of the London Mathematical Society. 2012 ; Vol. 86, No. 1. pp. 235-258.

Bibtex

@article{c79e336ba23847d7958f73b8645ba770,
title = "Dichotomy theorems for random matrices and closed ideals of operators on (\bigoplus_{n=1}^\infty\ell_1^n)_{c_0}.",
abstract = "We prove two dichotomy theorems about sequences of operators into L_1 given by random matrices. In the second theorem we assume that the entries of each random matrix form a sequence of independent, symmetric random variables. Then the corresponding sequence of operators either uniformly factor the identity operators on l_1^k for k = 1,2, ..., or uniformly approximately factor through c_0. The first theorem has a slightly weaker conclusion still related to factorization properties but makes no assumption on the random matrices. Indeed, it applies to operators defined on an arbitrary sequence of Banach spaces. These results provide information on the closed ideal structure of the Banach algebra of all operators on the c_0-direct sum of the finite-dimensional l_1-spaces l_1^1, l_1^2,..., l_1^n,...",
author = "Laustsen, {Niels Jakob} and Edward Odell and Thomas Schlumprecht and Andras Zsak",
note = "2000 Mathematics Subject Classification: 47L10 (primary), 46B09, 46B42, 47L20, 46B45 (secondary).",
year = "2012",
month = aug,
doi = "10.1112/jlms/jdr083",
language = "English",
volume = "86",
pages = "235--258",
journal = "Journal of the London Mathematical Society",
issn = "1469-7750",
publisher = "Oxford University Press",
number = "1",

}

RIS

TY - JOUR

T1 - Dichotomy theorems for random matrices and closed ideals of operators on (\bigoplus_{n=1}^\infty\ell_1^n)_{c_0}.

AU - Laustsen, Niels Jakob

AU - Odell, Edward

AU - Schlumprecht, Thomas

AU - Zsak, Andras

N1 - 2000 Mathematics Subject Classification: 47L10 (primary), 46B09, 46B42, 47L20, 46B45 (secondary).

PY - 2012/8

Y1 - 2012/8

N2 - We prove two dichotomy theorems about sequences of operators into L_1 given by random matrices. In the second theorem we assume that the entries of each random matrix form a sequence of independent, symmetric random variables. Then the corresponding sequence of operators either uniformly factor the identity operators on l_1^k for k = 1,2, ..., or uniformly approximately factor through c_0. The first theorem has a slightly weaker conclusion still related to factorization properties but makes no assumption on the random matrices. Indeed, it applies to operators defined on an arbitrary sequence of Banach spaces. These results provide information on the closed ideal structure of the Banach algebra of all operators on the c_0-direct sum of the finite-dimensional l_1-spaces l_1^1, l_1^2,..., l_1^n,...

AB - We prove two dichotomy theorems about sequences of operators into L_1 given by random matrices. In the second theorem we assume that the entries of each random matrix form a sequence of independent, symmetric random variables. Then the corresponding sequence of operators either uniformly factor the identity operators on l_1^k for k = 1,2, ..., or uniformly approximately factor through c_0. The first theorem has a slightly weaker conclusion still related to factorization properties but makes no assumption on the random matrices. Indeed, it applies to operators defined on an arbitrary sequence of Banach spaces. These results provide information on the closed ideal structure of the Banach algebra of all operators on the c_0-direct sum of the finite-dimensional l_1-spaces l_1^1, l_1^2,..., l_1^n,...

U2 - 10.1112/jlms/jdr083

DO - 10.1112/jlms/jdr083

M3 - Journal article

VL - 86

SP - 235

EP - 258

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

SN - 1469-7750

IS - 1

ER -