Spectrum of Quasi-Class (A,k) Operators
Joint Authors
Gao, Fugen
Fang, Xiaochun
Li, Xiaochun
Source
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-06-12
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
An operator T∈B(ℋ) is called quasi-class (A,k) if T∗k(|T2|−|T|2)Tk≥0 for a positive integer k, which is a common generalization of class A.
In this paper, firstly we consider some spectral properties of quasi-class (A,k) operators; it is shown that if T is a quasi-class (A,k) operator, then the nonzero points of its point spectrum and joint point spectrum are identical, the eigenspaces corresponding to distinct eigenvalues of T are mutually orthogonal, and the nonzero points of its approximate point spectrum and joint approximate point spectrum are identical.
Secondly, we show that Putnam's theorems hold for class A operators.
Particularly, we show that if T is a class A operator and either σ(|T|) or σ(|T∗|) is not connected, then T has a nontrivial invariant subspace.
American Psychological Association (APA)
Li, Xiaochun& Gao, Fugen& Fang, Xiaochun. 2011. Spectrum of Quasi-Class (A,k) Operators. ISRN Mathematical Analysis،Vol. 2011, no. 2011, pp.1-10.
https://search.emarefa.net/detail/BIM-470411
Modern Language Association (MLA)
Li, Xiaochun…[et al.]. Spectrum of Quasi-Class (A,k) Operators. ISRN Mathematical Analysis No. 2011 (2011), pp.1-10.
https://search.emarefa.net/detail/BIM-470411
American Medical Association (AMA)
Li, Xiaochun& Gao, Fugen& Fang, Xiaochun. Spectrum of Quasi-Class (A,k) Operators. ISRN Mathematical Analysis. 2011. Vol. 2011, no. 2011, pp.1-10.
https://search.emarefa.net/detail/BIM-470411
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-470411