A pointwise spectrum and representation of operators
A pointwise spectrum and representation of operators
For a self-adjoint operator <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A colon upper H right-arrow upper H"> <mml:semantics> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>:</mml:mo> <mml:mi>H</mml:mi> <mml:mo stretchy="false">→</mml:mo> <mml:mi>H</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">A:H\to H</mml:annotation> </mml:semantics> </mml:math> </inline-formula> commuting with an increasing family of projections <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper P equals left-parenthesis upper P Subscript …