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    Bounded Linear Operators and Bounded Invertibles

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    Let = c = C is a continuous function .
    Let = sup : , for each f in Define T: by

    (T ( ))(t) =
    for each t , and For each f in .

    a) Show that is a bounded linear operator on .
    b) Compute , For each n in N, and compute .
    c) Suppose that g . Show that the integral equation

    (t) - = g (t) for each t in
    has a solution f in

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    https://brainmass.com/math/linear-algebra/bounded-linear-operators-bounded-invertibles-35733

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    Let = c = C is a continuous function .
    Let = sup : , for each f in Define T: by
    (T ( ))(t) =
    for each t , and For each f in .

    a) Show that T is a bounded linear operator on .

    Proof:
    (1) First we want to prove T is a linear operator, that is, T(f + g)=T(f) + T(g), for any
    Actually, ...

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    Bounded Linear Operators and Bounded Invertibles are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

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