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2021•Mathematical Inequalities & ApplicationsOpen access

Sharp inequalities for the numerical radius of Hilbert space operators and operator matrices

Pintu Bhunia, Kallol Paul, Raj Kumar Nayak

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Abstract

We present new upper and lower bounds for the numerical radius of a bounded linear operator defined on a complex Hilbert space, which improve on the existing bounds. Among many other inequalities proved in this article, we show that for a non-zero bounded linear operator T on a complex Hilbert space H,

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What this paper is about

We present new upper and lower bounds for the numerical radius of a bounded linear operator defined on a complex Hilbert space, which improve on the existing bounds. Among many other inequalities proved in this article, we show that for a non-zero bounded linear operator T on a complex Hilbert space H,

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Available abstract

We present new upper and lower bounds for the numerical radius of a bounded linear operator defined on a complex Hilbert space, which improve on the existing bounds. Among many other inequalities proved in this article, we show that for a non-zero bounded linear operator T on a complex Hilbert space H,

Key concepts: Hilbert space, Operator matrix, Mathematics, Bounded function, RADIUS, Bounded operator, Operator (biology), Upper and lower bounds

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