- #1
SeM
Hi, I found in Kreyszig that if for any ##x_1\ and\ x_2\ \in \mathscr{D}(T)##
then an injective operator gives:
##x_1 \ne x_2 \rightarrow Tx_1 \ne Tx_2 ##
and
##x_1 = x_2 \rightarrow Tx_1 = Tx_2 ##If one has an operator T, is there an inequality or equality one can deduce from this, in order to check if an operator is surjective/injective or bijective? (In a similar manner to check for boundedness.)
Thanks!
then an injective operator gives:
##x_1 \ne x_2 \rightarrow Tx_1 \ne Tx_2 ##
and
##x_1 = x_2 \rightarrow Tx_1 = Tx_2 ##If one has an operator T, is there an inequality or equality one can deduce from this, in order to check if an operator is surjective/injective or bijective? (In a similar manner to check for boundedness.)
Thanks!