 Solution

ID: past-exam-of-the-functional-analysis-and-banach-and-c-algebras-course-of-the-university-of-oxford/2007/a/4/ii/solution

T_{1}

converge. From that subsequence extract another on which the images under

T_{2}

converge. Both image sequences, and hence their sum, converge on the latter subsequence. Thus $T_{1} + T_{2}$ is compact.

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