A Cantor Spectrum Diagonal in 𝒪₂

We prove the existence of a C <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="Superscript asterisk"> <mml:semantics> <mml:msup> <mml:mi/> <mml:mo> ∗ </mml:mo> </mml:msup> <mml:annotation encoding="application/x-tex">^*</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -diagonal in the Cuntz algebra <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper O 2"> <mml:semantics> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">O</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:annotation encoding="application/x-tex">\mathcal {O}_2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with spectrum homeomorphic to the Cantor space.