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Let $A_n \overset{SOT}{\to} A$ where $A$ is invertible. Does $A_n^{-1} \overset{SOT}{\to} A^{-1}$? Does $A_n^{-1} \overset{WOT}{\to} A^{-1}$?


EDIT: Forgot to mention $\{A,A_n\}\in\mathscr{B(H)}$ where $\mathscr{H}$ is a separable Hilbert space.

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    I had not noticed the "Linked" on the right. There is a complete (and interesting) answer by t.b., in case you had not noticed it as well.2012-05-21

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