• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.461-479
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• 2021

This paper includes a general version of Bessel multipliers in Hilbert C∗-modules. In fact, by combining analysis, an operator on the standard Hilbert C∗-module and synthesis, we reach so-called generalized Bessel multipliers. Because of their importance for applications, we are interested to determine cases when generalized multipliers are invertible. We investigate some necessary or sufficient conditions for the invertibility of such operators and also we look at which perturbation of parameters preserve the invertibility of them. Subsequently, our attention is on how to express the inverse of an invertible generalized frame multiplier as a multiplier. In fact, we show that for all frames, the inverse of any invertible frame multiplier with an invertible symbol can always be represented as a multiplier with an invertible symbol and appropriate dual frames of the given ones.

• Journal of the Korean Statistical Society
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• v.28 no.4
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• pp.503-513
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• 1999

The Bayes factor for the identification of stationary ARM(p,q) models is exactly computed using the Monte Carlo method. As priors are used the uniform prior for (\ulcorner,\ulcorner) in its stationarity-invertibility region, the Jefferys prior and the reference prior that are noninformative improper for ($\mu$,$\sigma$\ulcorner).

• Bulletin of the Korean Mathematical Society
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• v.28 no.2
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• pp.185-190
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• 1991

The concept of "almost invertibility modulo closed ideals" in L(X, Y) was introduced, implicitly, by Robin Harte [1, Theorem 3.9.5]. The aims of this note are to make the formal definition of "almost left and right invertible modulo closed ideals" operators and show that they form open sets.they form open sets.

• Bulletin of the Korean Mathematical Society
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• v.23 no.2
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• pp.91-102
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• 1986

A topological space (X,.tau.) is called invertible [7] if for each proper open set U in (X,.tau.) there exists a homoemorphsim h:(X,.tau.).rarw.(X,.tau.) such that h(X-U).contnd.U. Doyle and Hocking [7] and Levine [13], as well as others have investigated properties of invertible spaces. Recently, Crosseley and Hildebrand [5] have introduced the concept of semi-invertibility, which is weaker than that of invertibility, by replacing "homemorphism" in the definition of invertibility with "semihomemorphism", A space (X,.tau.) is said to be semi-invertible if for each proper semi-open set U in (X,.tau.) there exists a semihomemorphism h:(X,.tau.).rarw.(X,.tau.) such that h(X-U).contnd.U. The purpose of the present article is to introduce the class of almost-invertible spaces containing the class of semi-invertible spaces and to investigate its properties. One of the primary concerns will be to determine when a given local property in an almost-invertible space is also a global property. We point out that many of the results obtained can be applied in the cases of semi-invertible spaces and invertible spaces. For example, it is shown that if an invertible space (X,.tau.) has a nonempty open subset U which is, as a subspace, H-closed (resp. lightly compact, pseudocompact, S-closed, Urysohn, Urysohn-closed, extremally disconnected), then so is (X,.tau.).hen so is (X,.tau.).

• Korean Journal of Mathematics
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• v.3 no.2
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• pp.309-314
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• 1995

• Communications of the Korean Mathematical Society
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• v.8 no.3
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• pp.409-413
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• 1993

• Communications of the Korean Mathematical Society
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• v.8 no.3
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• pp.415-418
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• 1993

• The Mathematical Education
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• v.14 no.1
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• pp.27-27
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• 1975

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.1-13
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• 2022

The main aim of the article is to introduce new generalizations of Fredholm and Browder classes of spectra when the underlying Hilbert space is not necessarily separable and study their properties. To achieve the goal the notions of 𝛼-Browder operators, 𝛼-B-Fredholm operators, 𝛼-B-Browder operators and 𝛼-Drazin invertibility have been introduced. The relation of these classes of operators with their corresponding weighted spectra has been investigated. An equivalence of 𝛼-Drazin invertible operators with 𝛼-Browder operators and 𝛼-B-Browder operators has also been established. The weighted Browder spectrum of the sum of two bounded linear operators has been characterised in the case when the Hilbert space (not necessarily separable) is a direct sum of its closed invariant subspaces.

• Communications of the Korean Mathematical Society
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• v.8 no.2
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• pp.267-274
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• 1993