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

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Past exam of the functional Analysis and Banach and C*-Algebras course of the University of Oxford / 2007 / A / 4 / c / Solution by

Codex  0 2026-10-31

Compact. This operator is

B D

, where

D

is the compact diagonal operator in (a) and

B

is the bounded backward shift in (b). The composition property applies. Equivalently its tails have the same vanishing-coefficient finite-rank approximation.

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