Decompositions of block schur products

Research output: Contribution to journal › Journal article › Research › peer-review

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Decompositions of block schur products. / Christensen, Erik.

In: Journal of Operator Theory, Vol. 84, No. 1, 2020, p. 139-152.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Christensen, E 2020, 'Decompositions of block schur products', Journal of Operator Theory, vol. 84, no. 1, pp. 139-152. https://doi.org/10.7900/jot.2019feb16.2258

APA

Christensen, E. (2020). Decompositions of block schur products. Journal of Operator Theory, 84(1), 139-152. https://doi.org/10.7900/jot.2019feb16.2258

Vancouver

Christensen E. Decompositions of block schur products. Journal of Operator Theory. 2020;84(1):139-152. https://doi.org/10.7900/jot.2019feb16.2258

Author

Christensen, Erik. / Decompositions of block schur products. In: Journal of Operator Theory. 2020 ; Vol. 84, No. 1. pp. 139-152.

Bibtex

@article{31cde411182e42a3bbf4b151b557f646,
title = "Decompositions of block schur products",
abstract = "Given two m x n matrices A = (aij) and B = (bij) with entries in B(H) for some Hilbert space H, the Schur block product is the m x n matrix A□B:= (aijbij). There exists an mxn matrix S = (sij) with entries from B(H) such that S is a contraction operator and The analogus result for the block Schur tensor product defined by Horn and Mathias in [7] holds too. This kind of decomposition of the Schur product seems to be unknown, even for scalar matrices. Based on the theory of random matrices we show that the set of contractions S, which may appear in such a decomposition, is a thin set in the ball of all contractions.",
keywords = "Hadamard product, Polar decomposition, Random matrix, Row/column bounded, Schur product, Tensor product",
author = "Erik Christensen",
year = "2020",
doi = "10.7900/jot.2019feb16.2258",
language = "English",
volume = "84",
pages = "139--152",
journal = "Journal of Operator Theory",
issn = "0379-4024",
publisher = "Academia Romana Institutul de Matematica",
number = "1",

}

RIS

TY - JOUR

T1 - Decompositions of block schur products

AU - Christensen, Erik

PY - 2020

Y1 - 2020

N2 - Given two m x n matrices A = (aij) and B = (bij) with entries in B(H) for some Hilbert space H, the Schur block product is the m x n matrix A□B:= (aijbij). There exists an mxn matrix S = (sij) with entries from B(H) such that S is a contraction operator and The analogus result for the block Schur tensor product defined by Horn and Mathias in [7] holds too. This kind of decomposition of the Schur product seems to be unknown, even for scalar matrices. Based on the theory of random matrices we show that the set of contractions S, which may appear in such a decomposition, is a thin set in the ball of all contractions.

AB - Given two m x n matrices A = (aij) and B = (bij) with entries in B(H) for some Hilbert space H, the Schur block product is the m x n matrix A□B:= (aijbij). There exists an mxn matrix S = (sij) with entries from B(H) such that S is a contraction operator and The analogus result for the block Schur tensor product defined by Horn and Mathias in [7] holds too. This kind of decomposition of the Schur product seems to be unknown, even for scalar matrices. Based on the theory of random matrices we show that the set of contractions S, which may appear in such a decomposition, is a thin set in the ball of all contractions.

KW - Hadamard product

KW - Polar decomposition

KW - Random matrix

KW - Row/column bounded

KW - Schur product

KW - Tensor product

UR - http://www.scopus.com/inward/record.url?scp=85088254959&partnerID=8YFLogxK

U2 - 10.7900/jot.2019feb16.2258

DO - 10.7900/jot.2019feb16.2258

M3 - Journal article

AN - SCOPUS:85088254959

VL - 84

SP - 139

EP - 152

JO - Journal of Operator Theory

JF - Journal of Operator Theory

SN - 0379-4024

IS - 1

ER -

ID: 246725160