19.2.2.12 Convergence in Normed Spaces

Condition: Explore the sequence of operators \ (\ left \ {a_ {n} \ right \} \ subseteq l (x, x) \) for the processing and uniform (in normal) convergence in the following cases: a) \ (x = l_ {2}, \ quad a_ {n {n {n {n {n {n {n} X = \ Left (X_ {1}, \ LDOTS, X_ {N}, 0, \ LDOTS \ RIGHT), \ Quad X = \ LEFT (X_ {1}, X_ {2}, \ LDOTS \ RIGHT) \ In {2} \). b) \ (x = l_ {2}, \ quad a_ {n} x = \ left (x_ {n+1}, x_ {n+2}, 0, \ ldots \ right), \ quad x = \ left (x_ {1}, x_ {2}, \ ldots \ right) \ in l_ {2} \). c) \ (x = c [0.1], \ quad \ left (a_ {n} x \ right) (t) = t {n} (1-t) x (t), \ quad t \ in [0.1] \). e) \ (x = c [0.1], \ quad \ left (a_ {n} x \ right) (t) = t {n} x (t), \ quad t \ in [0.1] \).