Recent content by pyf

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    Finding the Adjoint of an Operator on a Hilbert Space

    I see. Well, this is the form that we've been given. Any ideas?
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    Finding the Adjoint of an Operator on a Hilbert Space

    The inner product is linear in its first argument, so I think so.
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    Finding the Adjoint of an Operator on a Hilbert Space

    Homework Statement Let H be a Hilbert space, with a in H and b in H. Let u be an operator on H with u(x)=<b,x>a Find the adjoint of u. Thanks! Homework Equations <ux,y>=<x,u*y> The Attempt at a Solution <ux,y>=<<b,x>a,y> = <b,x><a,y> = <b<a,y>,x> So it seems that all I...
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    Graduate Spectra of T and T* when T is a bounded linear operator

    I'm asking because they are equal for finite rank operators and I hope the relation is equally nice in infinite dimensions. :)
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    Graduate Spectra of T and T* when T is a bounded linear operator

    Hi, If T is a bounded linear operator on a Hilbert space, what can we say about the spectra of T and T* (\sigma(T)=\{\lambda:T-\lambda I is not invertible})?