Titlebook: Lectures on Numerical Radius Inequalities; Pintu Bhunia,Silvestru Sever Dragomir,Kallol Paul Book 2022 The Editor(s) (if applicable) and T

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,Numerical Radius Inequalities of Product of Operators,The spectral mapping theorem ensures that for a bounded linear operator . on a complex Hilbert space ., . where . is an analytic function on a domain containing . Unfortunately, there is no such relation for the numerical range of a bounded linear operator, that is, . for ..

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,Numerical Radius of Operator Matrices and Applications,Suppose . is a complex Hilbert space, and . is a bounded linear operator on

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,Operator Space Numerical Radius of , Block Matrices,In this chapter, following [57], the notion of complete numerical radius norm is studied and it is shown that the complete numerical radius norm of a completely bounded homomorphism can be computed in terms of the completely bounded norm of the map.

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,-Numerical Radius Inequalities in Semi-Hilbertian Spaces,Over the years, many mathematicians have studied different generalizations of the usual numerical radius of a bounded linear operator acting on a complex Hilbert space ., see [2, 147, 174].

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Research Problems,In this chapter, we present a number of research problems related to numerical range and numerical radius with various levels of difficulty. For most problems, we provide some references helping the reader to see the background needed to well understand and start thinking about them. Some of the problems given below are known and some are new.

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