A condition under which ๐ต=๐ด=๐*๐ต๐ follows from ๐ตโค๐ดโค๐*๐ต๐
Takateru Okayasu, Yasunori Ueta ยท Proceedings of the American Mathematical Society ยท 2006
We will give some sufficient conditions for a p p -hyponormal operator, p > 0 p>0 , to be normal, and a sufficient condition for a triplet of operators A A , B B , U U with A A , B B self-adjoint and U U unitary such that B โค A โค U โ B U B\le A\le U^*BU necessarily satisfies B = A = U โ B U B=A=U^*BU .