Berezin number and Berezin norm inequalities for operator matrices
Pintu Bhunia, Anirban Sen, Somdatta Barik, Kallol Paul
Abstract
We establish new upper bounds for the Berezin number and Berezin norm of operator matrices, which are refinements of existing bounds. Among other bounds, we prove that if A=[Aij] is an n×n operator matrix with Aij∈B(H) for i,j=1,2,…,n, then ‖A‖ber≤‖[‖Aij‖ber]‖ and ber(A)≤w([aij]), where aii=ber(Aii), aij=‖|Aij|+|Aji∗|‖ber1/2‖|Aji|+|Aij∗|‖ber1/2 if i<j and aij=0 if i>j. We also provide examples which illustrate these bounds for some concrete operators acting on the Hardy-Hilbert space.
Topics & Concepts
MathematicsHilbert spaceOperator (biology)Norm (philosophy)Matrix (chemical analysis)Algebra over a fieldPure mathematicsCombinatoricsLawBiochemistryGeneTranscription factorPolitical scienceChemistryRepressorMaterials scienceComposite materialHolomorphic and Operator TheoryMathematical Inequalities and ApplicationsMatrix Theory and Algorithms