Proper Improvement of Well-Known Numerical Radius Inequalities and Their Applications

New inequalities for the numerical radius of bounded linear operators defined on a complex Hilbert space H are given. In particular, it is established that if T is a bounded linear operator on a Hilbert space H then w 2 ( T ) ≤ min 0 ≤ α ≤ 1 α T ∗ T + ( 1 - α ) T T ∗ , where w ( T ) is the numerical...

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Veröffentlicht in:Resultate der Mathematik Jg. 76; H. 4
Hauptverfasser: Bhunia, Pintu, Paul, Kallol
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.12.2021
Schlagworte:
Mathematics
Mathematics and Statistics
bounded linear operator
26C10
zeros of polynomial
operator norm
47A12
Hilbert space
15A60
numerical radius
ISSN:1422-6383, 1420-9012
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Zusammenfassung:New inequalities for the numerical radius of bounded linear operators defined on a complex Hilbert space H are given. In particular, it is established that if T is a bounded linear operator on a Hilbert space H then w 2 ( T ) ≤ min 0 ≤ α ≤ 1 α T ∗ T + ( 1 - α ) T T ∗ , where w ( T ) is the numerical radius of T . The inequalities obtained here are non-trivial improvement of the well-known numerical radius inequalities. As an application we estimate bounds for the zeros of a complex monic polynomial.
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-021-01478-3