A note on rank-one operators in reflexive algebras
A note on rank-one operators in reflexive algebras
It is shown that if the invariant subspace lattice of a reflexive algebra <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper A"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">A</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathcal {A}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, acting on a separable Hilbert space, is both commutative and completely distributive, then the algebra generated by …