On k-Quasiclass A Operators. (13th December 2009)

• Record Type: Journal Article
• Authors: Gao, Fugen; Fang, Xiaochun
• Other Names: Takahasi Sin-Ei Academic Editor.
• Is Part Of: Journal of inequalities and applications. Volume 2009(2009)
• Publication Date: 2009-12-13
• Subjects: Inequalities (Mathematics) -- Periodicals; 512.97
• DOI: 10.1155/2009/921634
• Languages: English
• ISSNs: 1029-242X

Abstract

Abstract : An operatorT ∈ B ( ℋ ) is calledk -quasiclassA ifT ∗ k ( | T 2 | − | T | 2 ) T k ≥ 0 for a positive integerk, which is a common generalization of quasiclassA . In this paper, firstly we prove some inequalities of this class of operators; secondly we prove that ifT is ak -quasiclassA operator, thenT is isoloid andT − λ has finite ascent for all complex numberλ ; at last we consider the tensor product fork -quasiclassA operators.