• Title, Summary, Keyword: Fredholm operator

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REPRESENTATION OF INTEGRAL OPERATORS ON W22(Ω) OF REPRODUCING KERNELS

  • LEE, DONG-MYUNG;LEE, JEONG-GON;CUI, MING-GEN
    • Honam Mathematical Journal
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    • v.26 no.4
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    • pp.455-462
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    • 2004
  • We prove that if ${\mathbb{K}}^*$ is adjoint operator on $W_2{^2}({\Omega})$, then ${\mathbb{K}}^*v(t,\;{\tau})=,\;v(x,\;y){\in}W_2{^2}({\Omega})$ ; it is also related to the decomposition of solution of Fredholm equations.

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WEIGHTED COMPOSITION OPERATORS BETWEEN LP-SPACES

  • JABBARZADEH, M.R.
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.2
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    • pp.369-378
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    • 2005
  • In this paper we will consider the weighted composition operator $W=uC_{\varphi}$ between two different $L^p(X,\;\Sigma,\;\mu)$ spaces, generated by measurable and non-singular transformations $\varphi$ from X into itself and measurable functions u on X. We characterize the functions u and transformations $\varphi$ that induce weighted composition operators between $L^p-spaces$ by using some properties of conditional expectation operator, pair $(u,\;\varphi)$ and the measure space $(X,\;\Sigma,\;\mu)$. Also, Fredholmness of these type operators will be investigated.

ON WEIGHTED AND PSEUDO-WEIGHTED SPECTRA OF BOUNDED OPERATORS

  • Athmouni, Nassim;Baloudi, Hatem;Jeribi, Aref;Kacem, Ghazi
    • Communications of the Korean Mathematical Society
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    • v.33 no.3
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    • pp.809-821
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    • 2018
  • In the present paper, we extend the main results of Jeribi in [6] to weighted and pseudo-weighted spectra of operators in a nonseparable Hilbert space ${\mathcal{H}}$. We investigate the characterization, the stability and some properties of these weighted and pseudo-weighted spectra.

ON THE CLOSURE OF DOMINANT OPERATORS

  • Yang, Young-Oh
    • Communications of the Korean Mathematical Society
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    • v.13 no.3
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    • pp.481-487
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    • 1998
  • Let (equation omitted) denote the closure of the set (equation omitted) of dominant operators in the norm topology. We show that the Weyl spectrum of an operator T $\in$ (equation omitted) satisfies the spectral mapping theorem for analytic functions, which is an extension of [5, Theorem 1]. Also we show that an operator approximately equivalent to an operator of class (equation omitted) is of class (equation omitted).

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Spectral mapping theorem and Weyl's theorem

  • Yang, Young-Oh;Lee, Jin-A
    • Communications of the Korean Mathematical Society
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    • v.11 no.3
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    • pp.657-663
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    • 1996
  • In this paper we give some conditions under which the Weyl spectrum of an operator satisfies the spectral mapping theorem for analytic functions. Also we show that Weyl's theorem holds for p(T) where T is an operator of M-power class (N) and p is a polynomial on a neighborhood of $\sigam(T)$. Finally we answer an old question of Oberai.

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ON PREHERMITIAN OPERATORS

  • YOO JONG-KWANG;HAN HYUK
    • Communications of the Korean Mathematical Society
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    • v.21 no.1
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    • pp.53-64
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    • 2006
  • In this paper, we are concerned with the algebraic representation of the quasi-nilpotent part for prehermitian operators on Banach spaces. The quasi-nilpotent part of an operator plays a significant role in the spectral theory and Fredholm theory of operators on Banach spaces. Properties of the quasi-nilpotent part are investigated and an application is given to totally paranormal and prehermitian operators.

H-TOEPLITZ OPERATORS ON THE BERGMAN SPACE

  • Gupta, Anuradha;Singh, Shivam Kumar
    • Bulletin of the Korean Mathematical Society
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    • v.58 no.2
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    • pp.327-347
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    • 2021
  • As an extension to the study of Toeplitz operators on the Bergman space, the notion of H-Toeplitz operators B�� is introduced and studied. Necessary and sufficient conditions under which H-Toeplitz operators become co-isometry and partial isometry are obtained. Some of the invariant subspaces and kernels of H-Toeplitz operators are studied. We have obtained the conditions for the compactness and Fredholmness for H-Toeplitz operators. In particular, it has been shown that a non-zero H-Toeplitz operator can not be a Fredholm operator on the Bergman space. Moreover, we have also discussed the necessary and sufficient conditions for commutativity of H-Toeplitz operators.