Results 1 to 10 of about 57 (39)
ON QUASISIMILARITY FOR LOG-HYPONORMAL OPERATORS [PDF]
Glasgow Mathematical Journal, 2004 A bounded linear operator \(T\) defined on a infinite-dimensional complex Hilbert space \(\mathcal{H}\) is said to be {log-hyponormal} if and only if \(T\) is invertible and satisfies \(\log (T^*T)\geq \log (TT^*)\). The authors prove that if a restriction \(T_1\) of a log-hyponormal operator \(T\) to an invariant space is invertible, then \(T_1\) is ...
Jeon, I. H., Tanahashi, K., Uchiyama, A.
+22 more sources
TENSOR PRODUCTS OF LOG-HYPONORMAL OPERATORS [PDF]
Bulletin of the Korean Mathematical Society, 2005 Let \(A\) and \(B\) be invertible operators on a Hilbert space. The author proves that the tensor product \(A \otimes B\) of \(A\) and \(B\) is log-hyponormal if and only if \(A\) and \(B\) are both log-hyponormal. Tensor products of \(\omega\)-hyponormal and \(p\)-quasihyponormal operators are also studied.
exaly +2 more sources
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
TENSOR PRODUCTS OF LOG-HYPONORMAL AND OF CLASS $A(s,t)$ OPERATORS [PDF]
Glasgow Mathematical Journal, 2004 A bounded linear operator \(T\) defined on a complex Hilbert space \(\mathcal{H}\) is said to be {log-hyponormal} if \(T\) is invertible and satisfies \(\log (T^*T)\geq \log (TT^*)\). Let \(T=U| T| \) be the polar decomposition of a bounded operator \(T\) and for \(s,t>0\) let \(\widetilde{T}_{s,t}=| T| ^sU| T| ^t\) be the Aluthge transform of \(T\). \(
Tanahashi, Kôtarô, Chō, Muneo
openaire +2 more sources
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
Fuglede-Putnam's theorem for \boldmath p-hyponormal or \boldmath \rm{log}-hyponormal operators [PDF]
Glasgow Mathematical Journal, 2002 Let T be p-hyponormal or \rm{log}-hyponormal on a Hilbert space H . Then we have XT=T^*X whenever XT^*=TX for some X \in \scriptstyle{B}(\scriptstyle{H}). This is an extension of Patel's result. Also for p-hyponormal or \rm{log}-hyponormal T^*, dominant S and any X \in \scriptstyle{B}(\scriptstyle{H}) such that XT=SX, we have XT^*=S^*T.
Atsushi Uchiyama, Kôtarô Tanahashi
openaire +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