A note on w-hyponormal operators. Issue 1 (2002) - Chō, Muneo; Huruya, Tadasi; Kim, Young Ok
Abstract : LetT be aw -hyponormal operator with the polar decompositionT = U | T | . In this paper, we show the following: (1) IfT ˜ = | T | ( 1 / 2 ) U | T | ( 1 / 2 ) is normal, thenT is normal. (2) IfKer ( T ) = { 0 }, thenT 2 is alsow -hyponormal. (3) There exists aw -hyponormal operatorT such thatKer ( T ) ⊈ Ker ( T ∗ ) andKer ( T ) ⊉ Ker ( T ∗ ) .