Schur multiplier norm of product of matrices

schur multiplier norm of product of matrices

for a ∈ mn, the schur multiplier of a is defined as s a(x) =a ◦ x for all x ∈ mn and the spectral norm of s a can be stateas ∥s a∥ = supx,0 ∥a ∥x ◦x ∥ ∥. the other norm on s a can be definedas ∥s a∥ω = supx,0 ω(ω s( ax (x ) )) = supx,0 ωω (a (x ◦x ) ), where ω(a) standsfor the numerical radius of a. in this paper, we focus on therelation between the norm of schur multiplier of product of matric...

Schur product of matrices and numerical radius (range) preserving maps

Let F (A) be the numerical range or the numerical radius of a square matrix A. Denote by A◦B the Schur product of two matrices A and B. Characterizations are given for mappings on square matrices satisfying F (A ◦ B) = F (φ(A) ◦ φ(B)) for all matrices A and B. Analogous results are obtained for mappings on Hermitian matrices. 2000 Mathematics Subject Classification. 15A04, 15A18, 15A60

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

THE SPECTRAL NORM OF RANDOM INNER-PRODUCT KERNEL MATRICES By

We study the spectra of p×p random matrices K with off-diagonal (i, j) entry equal to n−1/2k(XT i Xj/n ), where Xi’s are the rows of a p× n matrix with i.i.d. entries and k is a scalar function. It is known that under mild conditions, as n and p increase proportionally, the empirical spectral measure of K converges to a deterministic limit μ. We prove that if k is a polynomial and the distribut...

Cartesian decomposition of matrices and some norm inequalities

Let ‎X be an ‎‎n-‎‎‎‎‎‎square complex matrix with the ‎Cartesian decomposition ‎‎X = A + i ‎B‎‎‎‎‎, ‎where ‎‎A ‎and ‎‎B ‎are ‎‎‎n ‎‎times n‎ ‎Hermitian ‎matrices. ‎It ‎is ‎known ‎that ‎‎$Vert X Vert_p^2 ‎leq 2(Vert A Vert_p^2 + Vert B Vert_p^2)‎‎‎$, ‎where ‎‎$‎p ‎‎geq 2‎$‎ ‎and ‎‎$‎‎Vert . Vert_p$ ‎is ‎the ‎Schatten ‎‎‎‎p-norm.‎ ‎‎ ‎‎In this paper‎, this inequality and some of its improvements ...

On the Nilpotent Multiplier of a Free Product