New trace norm inequalities for 2 × 2 blocks of diagonal matrices
نویسنده
چکیده
Several new trace norm inequalities are established for 2n × 2n block matrices, in the special case where the four n × n blocks are diagonal. Some of the inequalities are non-commutative analogs of Hanner's inequality , others describe the behavior of the trace norm under reordering of diagonal entries of the blocks.
منابع مشابه
A note on the Young type inequalities
In this paper, we present some refinements of the famous Young type inequality. As application of our result, we obtain some matrix inequalities for the Hilbert-Schmidt norm and the trace norm. The results obtained in this paper can be viewed as refinement of the derived results by H. Kai [Young type inequalities for matrices, J. Ea...
متن کاملUpper and lower bounds for numerical radii of block shifts
For an n-by-n complex matrix A in a block form with the (possibly) nonzero blocks only on the diagonal above the main one, we consider two other matrices whose nonzero entries are along the diagonal above the main one and consist of the norms or minimum moduli of the diagonal blocks of A. In this paper, we obtain two inequalities relating the numeical radii of these matrices and also determine ...
متن کاملCartesian 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 ...
متن کاملSome inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm
Let A = (an;k)n;k1 and B = (bn;k)n;k1 be two non-negative ma-trices. Denote by Lv;p;q;B(A), the supremum of those L, satisfying the followinginequality:k Ax kv;B(q) L k x kv;B(p);where x 0 and x 2 lp(v;B) and also v = (vn)1n=1 is an increasing, non-negativesequence of real numbers. In this paper, we obtain a Hardy-type formula forLv;p;q;B(H), where H is the Hausdor matrix and 0 < q p 1. Also...
متن کاملConcentration of Measure for Block Diagonal Matrices with Applications to Compressive Sensing
Theoretical analysis of randomized, compressive operators often depends on a concentration of measure inequality for the operator in question. Typically, such inequalities quantify the likelihood that a random matrix will preserve the norm of a signal after multiplication. When this likelihood is very high for any signal, the random matrices have a variety of known uses in dimensionality reduct...
متن کامل