Range-kernel characterizations of operators which are adjoint of each other
Range-kernel characterizations of operators which are adjoint of each other
Abstract We provide necessary and sufficient conditions for a pair S , T of Hilbert space operators in order that they satisfy $$S^*=T$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>S</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:mo>=</mml:mo> <mml:mi>T</mml:mi> </mml:mrow> </mml:math> and $$T^*=S$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>T</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:mo>=</mml:mo> <mml:mi>S</mml:mi> </mml:mrow> </mml:math> . As a …