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Bashyboy
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Homework Statement
Here is a link to the paper I am working through: http://www.ams.org/journals/proc/1970-025-01/S0002-9939-1970-0262849-9/S0002-9939-1970-0262849-9.pdf
Homework Equations
The Attempt at a Solution
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I am working on the first line of the proof. This is what I thus far understand: First they are relying on the fact that ##W(A)## is convex if and only if ##W(\mu A + \gamma I)##. Here is where I am unsure of things. I believe the first sentence is saying that we can stretch (or contract) the set by ##\mu## amount and translate it by ##\gamma## amount so that there exist vectors ##x_0## and ##x_1## such that ##\langle (\mu A + \gamma I)x_0,x_0 \rangle = 0## and ##\langle (\mu A + \gamma I)x_1,x_1 \rangle = 1## If this is true, then the problem can to reduce to assuming that we have an operator ##A## such that ##\langle Ax_0,x_0 \rangle = 0## and ##\langle Ax_1,x_1 \rangle = 1##.
Is that a correct interpretation? The reason I ask is, because I am interested in justifying this step, and I want to know precisely what I am proving.
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