Singular continuous spectrum is generic

Abstract

In a variety of contexts, we prove that singular continuous spectrum is generic in the sense that for certain natural complete metric spaces of operators, those with singular spectrum are a dense <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G Subscript delta"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>G</mml:mi> <mml:mi> δ </mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{G_\delta }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> .