Bounds of numerical radius of bounded linear operator using $t$-Aluthge transform

Bag, Santanu; Bhunia, Pintu; Paul, Kallol

doi:10.48550/arxiv.1904.12096

Cited by 5 publications

(5 citation statements)

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“…In this article, we obtain some upper bounds for the numerical radius of bounded linear operators and operator matrices. Using these bounds and the bounds obtained in [4,5,6,7,8] we obtain bounds for the radius of the disk with centre at origin that contains all the zeros of a complex monic polynomial. Also we show with numerical examples that these bounds obtained here improve on the existing bounds.…”

Section: Introductionmentioning

confidence: 99%

Estimations of zeros of a polynomial using numerical radius inequalities

Bhunia,

Bag,

Nayak

et al. 2020

Preprint

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Section: Introductionmentioning

confidence: 99%

Estimations of zeros of a polynomial using numerical radius inequalities

Bhunia,

Bag,

Nayak

et al. 2020

Preprint

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“…Kittaneh [9,10] improved on the above inequality to show that which improves on the above upper bounds. A lot of study has been done in this direction to improve upper and lower bounds for the numerical radius, and we refer the readers to [3,4,5,13,14,15], and the references therein, for a comprehensive idea of the current state of the art.…”

Section: Introductionmentioning

confidence: 99%

On a new norm on $\mathcal{B}({\mathcal{H}})$ and its applications to numerical radius inequalities

Sain¹,

Bhunia²,

Bhanja³

et al. 2020

Preprint

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We introduce a new norm on the space of bounded linear operators on a complex Hilbert space, which generalizes the numerical radius norm, the usual operator norm and the modified Davis-Wielandt radius. We study basic properties of this norm, including the upper and the lower bounds for it. As an application of the present study, we estimate bounds for the numerical radius of bounded linear operators. We illustrate with examples that our results improve on some of the important existing numerical radius inequalities.2010 Mathematics Subject Classification. Primary 47A30, 47A12; Secondary 47A63. Key words and phrases. Numerical radius; bounded linear operator; operator inequalities; Hilbert space.Dr. Debmalya Sain feels elated to acknowledge the remarkable contribution of his beloved friend Subhajyoti Sarkar in his life. Mr. Pintu Bhunia would like to thank UGC, Govt. of India for the financial support in the form of SRF. Prof. Kallol Paul would like to thank RUSA 2.0, Jadavpur University for partial support.

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“…Over the years many eminent mathematicians have studied and improved on the above inequality, to cite a few of them are [6,7,9,10,11,14,15]. Recently we [2,3,4,12,13] have developed some bounds for the numerical radius and applied them to estimate zeros of polynomials. In 1963, Bernau and Smithies [1] gave an elegant proof of the inequality w(T ) ≥ 1 2 T using parallelogram law.…”

Section: Introductionmentioning

confidence: 99%