Abstract
For bounded linear operators A and B on Hilbert spaces H and K, respectively, it is known that the numerical radii of A, B and A ⊗ B are related by the inequalities (Formula presented.). In this paper, we show that (1) if (Formula presented.), then w(A) = ρ(A) or w(B) = ρ(B), where ρ(·) denotes the spectral radius of an operator, and (2) if A is hyponormal, then (Formula presented.). Here (2) confirms a conjecture of Shiu's and is proven via dilating the hyponormal A to a normal operator N with the spectrum of N contained in that of A. The latter is obtained from the Sz.-Nagy-Foiaş dilation theory.
Original language | English |
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Pages (from-to) | 375-382 |
Number of pages | 8 |
Journal | Integral Equations and Operator Theory |
Volume | 78 |
Issue number | 3 |
DOIs | |
State | Published - Mar 2014 |
Keywords
- hyponormal operator
- numerical radius
- Numerical range
- tensor product