Some Upper Bounds for the Davis–Wielandt Radius of Hilbert Space Operators

In this paper, we give several inequalities involving the Davis–Wielandt radius and the numerical radii of Hilbert space operators. In particular, we show that if T is a bounded linear operator on a complex Hilbert space, then d w ( T ) ≤ ( w ( | T | 4 + | T | 8 ) + 2 w 2 ( | T | 2 T ) ) 1 4 , where...

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Bibliographic Details
Published in:Mediterranean journal of mathematics 2020-02, Vol.17 (1), Article 25
Main Authors: Zamani, Ali, Shebrawi, Khalid
Format: Article
Language:English
Subjects:
Hilbert space
Linear operators
Mathematics
Mathematics and Statistics
Upper bounds
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Summary:In this paper, we give several inequalities involving the Davis–Wielandt radius and the numerical radii of Hilbert space operators. In particular, we show that if T is a bounded linear operator on a complex Hilbert space, then d w ( T ) ≤ ( w ( | T | 4 + | T | 8 ) + 2 w 2 ( | T | 2 T ) ) 1 4 , where d w ( · ) and w ( · ) are the Davis–Wielandt radius and the numerical radius, respectively.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-019-1458-z