Abstract
We study properties of the numerical ranges of Foguel operators FT=[S⁎0TS], where S is the simple unilateral shift and T is some operator, both acting on ℓ2. Among other things, we show that (1) if T is nonzero compact, then the numerical radius w(FT) is strictly less than 1+(‖T‖/2), (2) if T is a diagonal unitary operator, then 5/2<w(FT)≤3/2, and (3) if T is a scalar operator aI, then the numerical range W(FT) is open and is not a circular disc unless a=0.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
