Decompositions of block schur products
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Documents
- DECOMPOSITIONS OF BLOCK SCHUR PRODUCTS
Accepted author manuscript, 197 KB, PDF document
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.
Original language | English |
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Journal | Journal of Operator Theory |
Volume | 84 |
Issue number | 1 |
Pages (from-to) | 139-152 |
ISSN | 0379-4024 |
DOIs | |
Publication status | Published - 2020 |
- Hadamard product, Polar decomposition, Random matrix, Row/column bounded, Schur product, Tensor product
Research areas
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