functional analysis

Theorem: Let X and y be two banach Spaces and suppose that T: X -Y is 1 ) bijective ,(il ) Continuous , (ii) linear Then I is continuous Exercise : If M and N ase normed spaces. Ten NXM is a normed space under the norm 11 - 1 1 : NXM - IR defined by 1 ( 2 7 ) 1 1 = 1 all + lly1/ Exercise : If N and M are bamack spaces then NXM is also a banach space