Results 1 to 10 of about 60 (41)
A Note on the Range of the Operator X ↦ TX−XT Defined on 𝒞2(ℋ)
International Journal of Mathematics and Mathematical Sciences, Volume 2009, Issue 1, 2009., 2009 We show how a proof of J. Stampfli can be extended to prove that the operator X ↦ TX−XT defined on the Hilbert‐Schmidt class, when T is an M‐hyponormal, p‐hyponormal, or log‐hyponormal operator, has a closed range if and only if σ(T) is finite.
Vasile Lauric, Manfred H. Moller
wiley +3 more sources
Hyponormality on a Weighted Bergman Space
Journal of Function Spaces, Volume 2020, Issue 1, 2020., 2020 A bounded Hilbert space operator T is hyponormal if T∗T − TT∗ is a positive operator. We consider the hyponormality of Toeplitz operators on a weighted Bergman space. We find a necessary condition for hyponormality in the case of a symbol of the form f+g¯ where f and g are bounded analytic functions on the unit disk.
Houcine Sadraoui +4 more
wiley +1 more source
On Properties of Class A(n) and n‐Paranormal Operators
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 Let n be a positive integer, and an operator T ∈ B(ℋ) is called a class A(n) operator if T1+n2/1+n≥|T|2 and n‐paranormal operator if T1+nx1/1+n≥||Tx|| for every unit vector x ∈ ℋ, which are common generalizations of class A and paranormal, respectively.
Xiaochun Li, Fugen Gao, Changsen Yang
wiley +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 2012, Issue 1, 2012., 2012 We prove some further properties of the operator T ∈ [nQN] (n‐power quasinormal, defined in Sid Ahmed, 2011). In particular we show that the operator T ∈ [nQN] satisfying the translation invariant property is normal and that the operator T ∈ [nQN] is not supercyclic provided that it is not invertible. Also, we study some cases in which an operator T ∈ [
Sid Ahmed Ould Ahmed Mahmoud +1 more
wiley +1 more source
Spectrum of Quasi‐Class (A,k) Operators
International Scholarly Research Notices, Volume 2011, Issue 1, 2011., 2011 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
Xiaochun Li +3 more
wiley +1 more source
Mathematics: The S. cerevisae for Natural Science Research
, 2012 International Journal of Mathematics and Mathematical Sciences, Volume 2012, Issue 1, 2012.
Shigeru Kanemitsu +3 more
wiley +1 more source
Extensions of the results on powers of
Journal of Inequalities and Applications, 2006 Firstly, we will show the following extension of the results on powers of -hyponormal and -hyponormal operators: let and be positive integers, if is -hyponormal for , then: (i) in case , and hold, (ii) in case , and hold.
Yang Changsen, Yuan Jiangtao
doaj
On powers of
Journal of Inequalities and Applications, 2000 A bounded linear operator on a Hilbert space is said to be -hyponormal for if , and is said to be log-hyponormal if is invertible and . Firstly, we shall show the following extension of our previous result: If is -hyponormal for , then and hold ...
Furuta Takayuki, Yanagida Masahiro
doaj
An invariant for certain operator algebras. [PDF]
Proc Natl Acad Sci U S A, 1974 Carey RW, Pincus JD.
europepmc +1 more source
Some of the next articles are maybe not open access.
Mosaic and Principal Functions of log-hyponormal Operators
Integral Equations and Operator Theory, 2004\textit{D. Xia} [``Spectral theory of hyponormal operators'' (Oper. Theory, Adv. Appl. 10, Birkhäuser Verlag, Basel) (1983; Zbl 0523.47012)] studied the mosaic and the principal function of semi-hyponormal operators with equal defect and nullity. A bounded linear operator \(T\) defined on a complex Hilbert space \(\mathcal{H}\) is said to be log ...
Takeaki Yamazaki +2 more
exaly +2 more sources