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Find a linear operator $T:C[0,1]\to C[0,1]$ whose spectrum is a given interval $[a,b]$.

How can I find a continuous function whose spectrum is exactly the given interval $[a,b]$, spectrum just states that spectrum lies in disk $\leq \|T\|$

Bruno B
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Vippul Jangira
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    Welcome to [math.se] SE. Take a [tour]. You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an [edit]): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance – Mr.Gandalf Sauron Jul 12 '23 at 08:16
  • What if you consider $f\mapsto ((b-a)x+a)f$ ? – Mr.Gandalf Sauron Jul 12 '23 at 08:25

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