http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
k-TH ROOTS OF p-HYPONORMAL OPERATORS
DUGGAL BHAGWATI P.,JEON IN Ho,KO AND EUNGIL Korean Mathematical Society 2005 대한수학회보 Vol.42 No.3
In this paper we prove that if T is a k-th root of a phyponormal operator when T is compact or T$^{n}$ is normal for some integer n > k, then T is (generalized) scalar, and that if T is a k-th root of a semi-hyponormal operator and have the property $\sigma$(T) is contained in an angle < 2$\pi$/k with vertex in the origin, then T is subscalar.
REMARKS ON SPECTRAL PROPERTIES OF p-HYPONORMAL AND LOG-HYPONORMAL OPERATORS
DUGGAL BHAGWATI P.,JEON, IN-HO Korean Mathematical Society 2005 대한수학회보 Vol.42 No.3
In this paper it is proved that for p-hyponormal or log-hyponormal operator A there exist an associated hyponormal operator T, a quasi-affinity X and an injection operator Y such that TX = XA and AY = YT. The operator A and T have the same spectral picture. We apply these results to give brief proofs of some well known spectral properties of p-hyponormal and loghyponormal operators, amongst them that the spectrum is a continuous function on these classes of operators.
Spectral properties of $p$-hyponormal and log-hyponormal operators
Bhagwati P. Duggal,전인호 대한수학회 2005 대한수학회보 Vol.42 No.3
In this paper it is proved that for p-hyponormal orlog-hyponormal operator A there exist an associated hyponormaloperator T, a quasi-anity X and an injection operator Y suchthat TX = XA and AY = Y T. The operator A and T have thesame spectral picture. We apply these results to give brief proofsof some well known spectral properties ofp-hyponormal and log-hyponormal operators, amongst them that the spectrum is a con-tinuous function on these classes of operators.
OPERATORS A, B FOR WHICH THE ALUTHGE TRANSFORM AB IS A GENERALISED n-PROJECTION
Bhagwati P. Duggal,김인현 대한수학회 2023 대한수학회보 Vol.60 No.6
A Hilbert space operator $A\in\B$ is a generalised \linebreak $n$-projection, denoted $A\in (G-n-P)$, if ${A^*}^n=A$. $(G-n-P)$-operators $A$ are normal operators with finitely countable spectra $\sigma(A)$, subsets of the set $\{0\}\cup\{\sqrt[n+1]{1}\}$. The Aluthge transform $\a$ of $A\in\B$ may be $(G-n-P)$ without $A$ being $(G-n-P)$. For doubly commuting operators $A, B\in\B$ such that $\sigma(AB)=\sigma(A)\sigma(B)$ and $\|A\|\|B\|\leq \left\|\c\right\|$, $\c\in (G-n-P)$ if and only if $A=\left\|\a\right\|(A_{00}\oplus(A_{0}\oplus A_u))$ and $B=\left\|\b\right\|(B_0\oplus B_u)$, where $A_{00}$ and $B_0$, and $A_0\oplus A_u$ and $B_u$, doubly commute, $A_{00}B_0$ and $A_0$ are 2 nilpotent, $A_u$ and $B_u$ are unitaries, $A^{*n}_u=A_u$ and $B^{*n}_u=B_u$. Furthermore, a necessary and sufficient condition for the operators $\alpha A$, $\beta B$, $\alpha \a$ and $\beta \b$, $\alpha=\frac{1}{\left\|\a\right\|}$ and $\beta=\frac{1}{\left\|\b\right\|}$, to be $(G-n-P)$ is that $A$ and $B$ are spectrally normaloid at $0$.
ON WEYL'S THEOREM FOR QUASI-CLASS A OPERATORS
Duggal Bhagwati P.,Jeon, In-Ho,Kim, In-Hyoun Korean Mathematical Society 2006 대한수학회지 Vol.43 No.4
Let T be a bounded linear operator on a complex infinite dimensional Hilbert space $\scr{H}$. We say that T is a quasi-class A operator if $T^*\|T^2\|T{\geq}T^*\|T\|^2T$. In this paper we prove that if T is a quasi-class A operator and f is a function analytic on a neigh-borhood or the spectrum or T, then f(T) satisfies Weyl's theorem and f($T^*$) satisfies a-Weyl's theorem.