4.22 Consider the left-shift operator on l (N), S : l (N) l (N), S(x1, x2,...)...

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4.22 Consider the left-shift operator on l (N), S : l (N) l (N), S(x1, x2,...) := (x2, x3, . . . ). (i) Show that S is a bounded linear operator. (ii) Show that S is not an isometry. (iii) Find the adjoint operator S*. 4.22 Consider the left-shift operator on l (N), S : l (N) l (N), S(x1, x2,...) := (x2, x3, . . . ). (i) Show that S is a bounded linear operator. (ii) Show that S is not an isometry. (iii) Find the adjoint operator S*.