Decompositions of block schur products
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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
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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