Numerical radius inequalities for products and sums of semi-Hilbertian space operators

Pintu Bhunia; Kais Feki; Kallol Paul

Numerical radius inequalities for products and sums of semi-Hilbertian space operators

Functional Analysis 2020-12-23 v1

Authors: Pintu Bhunia , Kais Feki , Kallol Paul

Abstract

New inequalities for the $A$ -numerical radius of the products and sums of operators acting on a semi-Hilbert space, i.e. a space generated by a positive semidefinite operator $A$ , are established. In particular, it is proved for operators $T$ and $S,$ having $A$ -adjoint, that $\omega_A(TS) \leq \frac{1}{2}\omega_A(ST)+\frac{1}{4}\Big(\|T\|_A\|S\|_A+\|TS\|_A\Big),$ where $\omega_A(T)$ and $\|T\|_A$ denote the $A$ -numerical radius and the $A$ -operator seminorm of an operator $T$ .

Keywords

numerical radius inequalities semi-hilbert space operators positive semidefinite operator a-numerical radius a-operator seminorm schmidt decomposition

Cite

@article{arxiv.2012.12034,
  title  = {Numerical radius inequalities for products and sums of semi-Hilbertian space operators},
  author = {Pintu Bhunia and Kais Feki and Kallol Paul},
  journal= {arXiv preprint arXiv:2012.12034},
  year   = {2020}
}

Numerical radius inequalities for products and sums of semi-Hilbertian space operators

Abstract

Keywords

Cite

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