• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.91-97
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• 1998

In this paper we study the Weyl spectrum of weight $\alpha, \omega_\alpha(T)$, of an operator T acting on an infinite dimensional Hilbert space. Main results are as follows. Firstly, we show that the Weyll spectrum of weight $\alpha$ of a polynomially $\alpha$-compact operator is finite, and that similarity preserves polynomial $\alpha$-compactness and the $\alpha$-Weyl's theorem both. Secondly, we give a sufficient condition for an operator to be the sum of an unitary and a $\alpha$-compact operators.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.565-570
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• 2012

In this note we investigate Weyl's theorem for *-paranormal operators on a separable infinite dimensional Hilbert space. We prove that if T is a *-paranormal operator satisfying Property $(E)-(T-{\lambda}I)H_T(\{{\lambda}\})$ is closed for each ${\lambda}{\in}{\mathbb{C}}$, where $H_T(\{{\lambda}\})$ is a local spectral subspace of T, then Weyl's theorem holds for T.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.899-910
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• 2012

Let $\mathcal{H}$ be a complex separable infinite dimensional Hilbert space. In this paper, a necessary and sufficient condition is given for an operator T on $\mathcal{H}$ to satisfy that $f(T)$ obeys generalized Weyl's theorem for each function $f$ analytic on some neighborhood of ${\sigma}(T)$. Also we investigate the stability of generalized Weyl's theorem under (small) compact perturbations.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1167-1176
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• 2022

In this paper, we study Einstein-type manifolds generalizing static spaces and V-static spaces. We prove that if an Einstein-type manifold has non-positive complete divergence of its Weyl tensor and non-negative complete divergence of Bach tensor, then M has harmonic Weyl curvature. Also similar results on an Einstein-type manifold with complete divergence of Riemann tensor are proved.

• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.149-155
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• 1998

In this paper, we construct the minimal set of generators which generate the subgroup T of the Weyl group of Kac-Moody algebra.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.571-575
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• 2002

In this paper we show that Weyl's theorem holds for f(T) when an Hilbert space operator T is “algebraically totally-paranormal” and f is any analytic function on an open neighbor-hood of the spectrum of T.

• Communications of the Korean Mathematical Society
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• v.16 no.2
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• pp.235-241
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• 2001

In this paper we study some properties of he joint Weyl and Browder spectra for the slightly larger classes containing doubly commuting n-tuples of hyponormal operators.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.53-62
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• 2000

In this paper we explore relations between joint Weyl and Browder spectra. Also, we give a spectral characterization of the Taylor-Browder spectrum for special classes of doubly commuting n-tuples of operators and then give a partial answer to Duggal's question.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.899-909
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• 2006

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.