Real isomorphic complex Banach spaces need not be complex isomorphic
Real isomorphic complex Banach spaces need not be complex isomorphic
It is shown that complex Banach spaces may be isomorphic as real spaces and not as complex spaces. If <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding="application/x-tex">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a complex Banach space, denote <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X overbar"> <mml:semantics> <mml:mover> <mml:mi>X</mml:mi> <mml:mo accent="false">¯<!-- …