Decompositions of block schur products

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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 languageEnglish
JournalJournal of Operator Theory
Issue number1
Pages (from-to)139-152
Publication statusPublished - 2020

    Research areas

  • Hadamard product, Polar decomposition, Random matrix, Row/column bounded, Schur product, Tensor product

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