http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
A NOTE ON *-PARANORMAL OPERATORS AND RELATED CLASSES OF OPERATORS
Kotaro Tanahashi,Atsushi Uchiyama 대한수학회 2014 대한수학회보 Vol.51 No.2
We shall show that the Riesz idempotent E of every ∗- paranormal operator T on a complex Hilbert space H with respect to each isolated point of its spectrum (T) is self-adjoint and satisfies EH = ker(T − ) = ker(T − )∗. Moreover, Weyl’s theorem holds for ∗-paranormal operators and more general for operators T satisfying the norm condition ∥Tx∥n ≤ ∥Tnx∥kx∥n−1 for all x ∈ H. Finally, for this more general class of operators we find a sufficient condition such that EH = ker(T − ) = ker(T − )∗ holds. We shall show that the Riesz idempotent E of every ∗- paranormal operator T on a complex Hilbert space H with respect to each isolated point of its spectrum (T) is self-adjoint and satisfies EH = ker(T − ) = ker(T − )∗. Moreover, Weyl’s theorem holds for ∗-paranormal operators and more general for operators T satisfying the norm condition ∥Tx∥n ≤ ∥Tnx∥∥x∥n−1 for all x ∈ H. Finally, for this more general class of operators we find a sufficient condition such that EH = ker(T − ) = ker(T − )∗ holds.
Fuglede-Putnam theorem for $p$-hyponormal or class ${\mathcal Y}$
Salah Mecheri,Kotaro Tanahashi,Atsushi Uchiyama 대한수학회 2006 대한수학회보 Vol.43 No.4
We say operatorsA;Bon Hilbert space satisfy Fuglede-Putnam theorem ifAX = XB for someX implies AX = XB.We show that if either (1)A is p-hyponormal and Bis a classYoperator or (2)A is a classY operator and Bis p-hyponormal,then A;B satisfy Fuglede-Putnam theorem.
FUGLEDE-PUTNAM THEOREM FOR p-HYPONORMAL OR CLASS y OPERATORS
Mecheri, Salah,Tanahashi, Kotaro,Uchiyama, Atsushi Korean Mathematical Society 2006 대한수학회보 Vol.43 No.4
We say operators A, B on Hilbert space satisfy Fuglede-Putnam theorem if AX = X B for some X implies $A^*X=XB^*$. We show that if either (1) A is p-hyponormal and $B^*$ is a class y operator or (2) A is a class y operator and $B^*$ is p-hyponormal, then A, B satisfy Fuglede-Putnam theorem.
Cho, Muneo,Lee, Ji Eun,Tanahashi, Kotaro,Tomiyama, Jun Department of Mathematics 2018 Kyungpook mathematical journal Vol.58 No.4
In this paper first we show properties of isosymmetric operators given by M. Stankus [13]. Next we introduce an [m, C]-symmetric operator T on a complex Hilbert space H. We investigate properties of the spectrum of an [m, C]-symmetric operator and prove that if T is an [m, C]-symmetric operator and Q is an n-nilpotent operator, respectively, then T + Q is an [m + 2n - 2, C]-symmetric operator. Finally, we show that if T is [m, C]-symmetric and S is [n, D]-symmetric, then $T{\otimes}S$ is [m + n - 1, $C{\otimes}D$]-symmetric.