%0 Journal Article %T Schur multiplier norm of product of matrices %J Wavelet and Linear Algebra %I Vali-e-Asr university of Rafsanjan %Z 2383-1936 %A Khosravi, M. %A Sheikhhosseini, A. %D 2015 %\ 09/01/2015 %V 2 %N 1 %P 49-54 %! Schur multiplier norm of product of matrices %K Schur multiplier %K Schur product %K Geometric product %K Positive semidefinite matrix %K Numerical radius %R %X For A ∈ M n, the Schur multiplier of A is defined as S A(X) = A ◦ X for all X ∈ M n and the spectral norm of S A can be state as ∥S A∥ = supX,0 ∥A ∥X ◦X ∥ ∥. The other norm on S A can be defined as ∥S A∥ω = supX,0 ω(ω S( AX (X ) )) = supX,0 ωω (A (X ◦X ) ), where ω(A) stands for the numerical radius of A. In this paper, we focus on the relation between the norm of Schur multiplier of product of matrices and the product of norm of those matrices. This relation is proved for Schur product and geometric product and some applications are given. Also we show that there is no such relation for operator product of matrices. Furthermore, for positive definite matrices A and B with ∥S A∥ω ⩽ 1 and ∥S B∥ω ⩽ 1, we show that A♯B = n(I − Z)1/2C(I + Z)1/2, for some contraction C and Hermitian contraction Z. %U https://wala.vru.ac.ir/article_14269_e9a1dc6d7c67b98d454cd7225318629e.pdf