A note on w-hyponormal operators. Issue 1 (2002)

• Record Type: Journal Article
• Authors: Chō, Muneo; Huruya, Tadasi; Kim, Young Ok
• Is Part Of: Journal of inequalities and applications. Volume 7:Issue 1(2002)
• Page Start: 1
• Page End: 10
• Publication Date: 2002
• Subjects: w-hyponormal operator; p-hyponormal operator; Furuta inequality; Inequalities (Mathematics) -- Periodicals; 512.97
• DOI: 10.1155/S1025583402000012
• Languages: English
• ISSNs: 1029-242X

Abstract

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 ∗ ) .