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- Title
Numerical radius inequalities and estimation of zeros of polynomials.
- Authors
Bhunia, Pintu; Jana, Suvendu; Paul, Kallol
- Abstract
Let A be a bounded linear operator defined on a complex Hilbert space and let | A | = (A * A) 1 2 . Among other refinements of the well-known numerical radius inequality w 2 (A) ≤ 1 2 ∥ A * A + A A * ∥ , we show that w 2 (A) ≤ 1 4 w 2 (| A | + i | A * |) + 1 8 ∥ | A | 2 + | A * | 2 ∥ + 1 4 w (| A | | A * |) ≤ 1 2 ∥ A * A + A A * ∥ . Also, we develop inequalities involving the numerical radius and the spectral radius for the sum of the product operators, from which we derive the inequalities w p (A) ≤ 1 2 w ( | A | p + i | A * | p ) ≤ ∥ A ∥ p for all p ≥ 1 . Further, we derive new bounds for the zeros of complex polynomials.
- Subjects
POLYNOMIALS; HILBERT space; LINEAR operators; RADIUS (Geometry)
- Publication
Georgian Mathematical Journal, 2023, Vol 30, Issue 5, p671
- ISSN
1072-947X
- Publication type
Article
- DOI
10.1515/gmj-2023-2037