[Solution Library] Let E be a Banach space and let A,B ∈ L(E) . Define T:L(E)→ L(E) by TX=AXB Show that T is a linear operator and is bounded with
Question: Let E be a Banach space and let \(A,B\in L\left( E \right)\) . Define \(T:L\left( E \right)\to L\left( E \right)\) by
\[TX=AXB\]Show that T is a linear operator and is bounded with respect to the operator norm on L(E), with \(||T||\le ||A||||B||\) .
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