19.3.26 Linear Operators

Condition: Find the operator conjugated to the operator \ (a: l_ {1} \ rightarrow l_ {1} \) if: a) \ (a x = \ left (x_ {1}, \ ldots, x_ {n}, 0, \ ldots \ right) \), b) \ (a x = \ left (\ lambda_ {1} x_ {1}, \ lambda_ {2} x_ {2}, \ ldots \ right), \ quad \ lefta_ {n} \ leq 1 \ Forall n \), c) \ (a x = \ left (0, x_ {1}, x_ {2}, \ ldots \ right) \), d) \ (a x = \ left (x_ {2}, x_ {3}, \ ldots \ right) \)