Answer Happy

Posted: **Tue Jul 12, 2022 12:46 pm**

: 1 Let A B H And An Nen A Sequence In B H A Show That If An Nen Converges To A In Norm Then Also Strongly B S 1 (12.09 KiB) Viewed 43 times

1. Let A B(H) and (An)neN a sequence in B(H). (a) Show that if (An)neN converges to A in norm, then also strongly. (b) Show that if (An)neN converges to A strongly, then also weakly. (c) Give examples that show that the converses of (a) and (b) do not hold.