 Telescoping bound for products of operators

ID: telescoping-bound-for-products-of-operators

A_{j}

and

B_{j}

have operator norm at most one, then inserting and subtracting one factor at a time gives

\prod_{j = 1}^{m} A_{j} - \prod_{j = 1}^{m} B_{j} \leq \sum_{j = 1}^{m} ∥ A_{j} - B_{j} ∥.

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