Statistics Solutions

(See Solution) 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 respect

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 \(L\left( E \right)\), with \(||T||\le ||A||\,||B||\).

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