2018/11/08 by Christensen, Erik
#15A69 #46L07 #46N50 #47L25 #81P68 #81T05 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1811.03668
Given two m x n matrices A = (aij) and B=(bij) with entries in B(H), the Schur block product is the m x n matrix A \square B := (aijbij). There exists an m x n contraction matrix S = (sij), such that A \square B = diag(AA*)^(1/2) S diag(B*B)^(1/2). This decomposition is also valid for the block Schur tensor product. It is shown, via the theory of random matrices, that the set of contractions S, which may appear in such a decomposition, is a very thin subset of the unit ball of Mn(B(H)).