• Title/Summary/Keyword: B-operator

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CHARACTERIZATION OF STRICTLY OPERATOR SEMI-STABLE DISTRIBUTIONS

  • Choi, Gyeong-Suk
    • Journal of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.101-123
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    • 2001
  • For a linear operator Q from R(sup)d into R(sup)d and 0$\alpha$ and parameter b on the other. characterization of strictly (Q,b)-semi-stable distributions among (Q,b)-semi-stable distributions is made. Existence of (Q,b)-semi-stable distributions which are not translation of strictly (Q,b)-semi-stable distribution is discussed.

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ON CHAOTIC OPERATOR ORDER $A\;{\gg}\;C\;{\gg}\;B$ IN HILBERT SPACES

  • Lin, C.S.
    • East Asian mathematical journal
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    • v.24 no.1
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    • pp.67-79
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    • 2008
  • In this paper, we characterize the chaotic operator order $A\;{\gg}\;C\;{\gg}\;B$. Consequently all other possible characterizations follow easily. Some satellite theorems of the Furuta inequality are naturally given. And finally, using results of characterizing $A\;{\gg}\;C\;{\gg}\;B$, and by the Douglas's majorization and factorization theorem we are able to characterize the chaotic operator order $A\;{\gg}\;B$ in terms of operator equalities.

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REPRESENTATION OF OPERATOR SEMI-STABLE DISTRIBUTIONS

  • Choi, Gyeong-Suk
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.1
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    • pp.135-152
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    • 2000
  • For a linear operator Q from $R^{d}\; into\; R^{d},\; {\alpha}\;>0\; and\ 0-semi-stability and the operater semi-stability of probability measures on $R^{d}$ are defined. Characterization of $(Q,b,{\alpha})$-semi-stable Gaussian distribution is obtained and the relationship between the class of $(Q,b,{\alpha})$-semi-stable non-Gaussian distributions and that of operator semistable distributions is discussed.

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TOEPLITZ TYPE OPERATOR IN ℂn

  • Choi, Ki Seong
    • Journal of the Chungcheong Mathematical Society
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    • v.27 no.4
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    • pp.697-705
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    • 2014
  • For a complex measure ${\mu}$ on B and $f{\in}L^2_a(B)$, the Toeplitz operator $T_{\mu}$ on $L^2_a(B,dv)$ with symbol ${\mu}$ is formally defined by $T_{\mu}(f)(w)=\int_{B}f(w)\bar{K(z,w)}d{\mu}(w)$. We will investigate properties of the Toeplitz operator $T_{\mu}$ with symbol ${\mu}$. We define the Toeplitz type operator $T^r_{\psi}$ with symbol ${\psi}$, $$T^r_{\psi}f(z)=c_r\int_{B}\frac{(1-{\parallel}w{\parallel}^2)^r}{(1-{\langle}z,w{\rangle})^{n+r+1}}{\psi}(w)f(w)d{\nu}(w)$$. We will also investigate properties of the Toeplitz type operator with symbol ${\psi}$.

On Normal Products of Selfadjoint Operators

  • Jung, Il Bong;Mortad, Mohammed Hichem;Stochel, Jan
    • Kyungpook Mathematical Journal
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    • v.57 no.3
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    • pp.457-471
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    • 2017
  • A necessary and sufficient condition for the product AB of a selfadjoint operator A and a bounded selfadjoint operator B to be normal is given. Various properties of the factors of the unitary polar decompositions of A and B are obtained in the case when the product AB is normal. A block operator model for pairs (A, B) of selfadjoint operators such that B is bounded and AB is normal is established. The case when both operators A and B are bounded is discussed. In addition, the example due to Rehder is reexamined from this point of view.

ADDITIVITY OF LIE MAPS ON OPERATOR ALGEBRAS

  • Qian, Jia;Li, Pengtong
    • Bulletin of the Korean Mathematical Society
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    • v.44 no.2
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    • pp.271-279
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    • 2007
  • Let A standard operator algebra which does not contain the identity operator, acting on a Hilbert space of dimension greater than one. If ${\Phi}$ is a bijective Lie map from A onto an arbitrary algebra, that is $${\phi}$$(AB-BA)=$${\phi}(A){\phi}(B)-{\phi}(B){\phi}(A)$$ for all A, B${\in}$A, then ${\phi}$ is additive. Also, if A contains the identity operator, then there exists a bijective Lie map of A which is not additive.

Generalized Weyl's Theorem for Some Classes of Operators

  • Mecheri, Salah
    • Kyungpook Mathematical Journal
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    • v.46 no.4
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    • pp.553-563
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    • 2006
  • Let A be a bounded linear operator acting on a Hilbert space H. The B-Weyl spectrum of A is the set ${\sigma}_{B{\omega}}(A)$ of all ${\lambda}{\in}\mathbb{C}$ such that $A-{\lambda}I$ is not a B-Fredholm operator of index 0. Let E(A) be the set of all isolated eigenvalues of A. Recently in [6] Berkani showed that if A is a hyponormal operator, then A satisfies generalized Weyl's theorem ${\sigma}_{B{\omega}}(A)={\sigma}(A)$\E(A), and the B-Weyl spectrum ${\sigma}_{B{\omega}}(A)$ of A satisfies the spectral mapping theorem. In [51], H. Weyl proved that weyl's theorem holds for hermitian operators. Weyl's theorem has been extended from hermitian operators to hyponormal and Toeplitz operators [12], and to several classes of operators including semi-normal operators ([9], [10]). Recently W. Y. Lee [35] showed that Weyl's theorem holds for algebraically hyponormal operators. R. Curto and Y. M. Han [14] have extended Lee's results to algebraically paranormal operators. In [19] the authors showed that Weyl's theorem holds for algebraically p-hyponormal operators. As Berkani has shown in [5], if the generalized Weyl's theorem holds for A, then so does Weyl's theorem. In this paper all the above results are generalized by proving that generalizedWeyl's theorem holds for the case where A is an algebraically ($p,\;k$)-quasihyponormal or an algebarically paranormal operator which includes all the above mentioned operators.

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Rank-preserver of Matrices over Chain Semiring

  • Song, Seok-Zun;Kang, Kyung-Tae
    • Kyungpook Mathematical Journal
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    • v.46 no.1
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    • pp.89-96
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    • 2006
  • For a rank-1 matrix A, there is a factorization as $A=ab^t$, the product of two vectors a and b. We characterize the linear operators that preserve rank and some equivalent condition of rank-1 matrices over a chain semiring. We also obtain a linear operator T preserves the rank of rank-1 matrices if and only if it is a form (P, Q, B)-operator with appropriate permutation matrices P and Q, and a matrix B with all nonzero entries.

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REMARKS ON GAUSSIAN OPERATOR SEMI-STABLE DISTRIBUTIONS

  • Chae, Hong Chul;Choi, Gyeong Suk
    • Korean Journal of Mathematics
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    • v.8 no.2
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    • pp.111-119
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    • 2000
  • For a linear operator Q from $R^d$ into $R^d$. ${\alpha}$ > 0 and 0 < $b$ < 1, the Gaussian (Q, $b$, ${\alpha}$)-semi-stability of probability measures on $R^d$ is investigated.

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NOTES ON BERGMAN PROJECTION TYPE OPERATOR RELATED WITH BESOV SPACE

  • CHOI, KI SEONG
    • Journal of the Chungcheong Mathematical Society
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    • v.28 no.3
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    • pp.473-482
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    • 2015
  • Let Qf be the maximal derivative of f with respect to the Bergman metric $b_B$. In this paper, we will find conditions such that $(1-{\parallel}z{\parallel})^s(Qf)^p(z)$ is bounded on B. We will also find conditions such that Bergman projection type operator $P_r$ is bounded operator from $L^p(B,d{\mu}_r)$ to the holomorphic Besov p-space Bs $B^s_p(B)$ with weight s.