We first show some properties of such operators and give an explit description about the image of a linear bounded operator on a linear normed space. Then based on these results, we show the mean ergordic theorem on a C*-bial-gebra and get a sufficient and necessary condition for a linear functional to be Haar measure. Finally we discuss the sufficent conditions for the existence of Haar measure on C*-bialgebras.

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Your friend mrs rong has still not called me to find out what i need to do to get you over here so i will find out through the internet what i have to do and get over there to marry you as soon as i can hopefully it wont take long for your k-1 visa to get done after we marry but i must tell you that i live in arizona and the only snow you will see is on t.v.

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