Exotic closed subideals of algebras of bounded operators
Exotic closed subideals of algebras of bounded operators
We exhibit a Banach space <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Z"> <mml:semantics> <mml:mi>Z</mml:mi> <mml:annotation encoding="application/x-tex">Z</mml:annotation> </mml:semantics> </mml:math> </inline-formula> failing the approximation property, for which there is an uncountable family <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper F"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="script">F</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathscr F</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of closed …