Frobenius norm inequalities of commutators based on different products

Bergman Commutators and Norm Ideals

Let P be the orthogonal projection from L(B, dv) onto the Bergman space La(B, dv) of the unit ball in C . In this paper we characterize the membership of commutators of the form [Mf , P ] in the norm ideal CΦ, where the symmetric gauge function Φ is allowed to be arbitrary.

Improving approximate inverses based on Frobenius norm minimization

Approximate inverses, based on Frobenius norm minimization, of real nonsingular matrices are analyzed from a purely theoretical point of view. In this context, this paper provides several sufficient conditions, that assure us the possibility of improving (in the sense of the Frobenius norm) some given approximate inverses. Moreover, the optimal approximate inverses of matrix A ∈ R, among all ma...

Frobenius-norm-based measures of quantum coherence and asymmetry

We formulate the Frobenius-norm-based measures for quantum coherence and asymmetry respectively. In contrast to the resource theory of coherence and asymmetry, we construct a natural measure of quantum coherence inspired from optical coherence theory while the group theoretical approach is employed to quantify the asymmetry of quantum states. Besides their simple structures and explicit physica...

Powers of Commutators as Products of Squares

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 ...