Polar decomposition approach to Reid's inequality. Issue 6 (2002)

• Record Type: Journal Article
• Authors: Lin, C.-S.
• Is Part Of: Journal of inequalities and applications. Volume 7:Issue 6(2002)
• Page Start: 779
• Page End: 785
• Publication Date: 2002
• Subjects: Polar decomposition; Reid's inequality; Spectral radius; Inequalities (Mathematics) -- Periodicals; 512.97
• DOI: 10.1155/S1025583402000401
• Languages: English
• ISSNs: 1029-242X

Abstract

Abstract : IfS ≥ 0 andS K is Hermitian, then| ( S K x, x ) ≤ ‖ K ‖ ( S x, x ) holds for allx ∈ H, which is known as Reid's inequality and was sharpened by Halmos in which‖ K ‖ was replaced byr ( K ), the spectral radius ofK . In this article we present generalizations of Reid's and Halmos' inequalities via polar decomposition approach. Conditions onS andS K are relaxed. Theorem regards Reid-type inequalities, and Theorem 2 contains Halmos-type inequalities.