2016/04/17 by Haria, Kalpesh J., Maji, Amit, Sarkar, Jaydeb · 1 citation
#47A13 #47A15 #47A20 #47A68 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1604.04858
Let A = (A1, …, An) and B = (B1, …, Bn) be row contractions on H1 and H2, respectively, and X be a row operator from ⊕i=1n H2 to H1. Let DA^* = (I - A A^*)(1)/(2) and DB = (I - B^* B)(1)/(2) and ΘT be the characteristic function of T = \beginbmatrix A& DA^*L DB 0 & B \endbmatrix. Then ΘT coincides with the product of the characteristic function ΘA of A, the Julia-Halmos matrix corresponding to L and the characteristic function ΘB of B. More precisely, ΘT coincides with \beginbmatrix ΘB amp; 0
0 amp; I \endbmatrix (IΓ⊗ \beginbmatrix L^* amp; (I - L^* L)(1)/(2)
(I - L L^*)(1)/(2) amp; - L \endbmatrix) \beginbmatrix ΘA amp; 0
0amp; I\endbmatrix, where Γ is the full Fock space. Similar results hold for constrained row contractions.