• 충청수학회지
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• 제36권1호
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• pp.13-23
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• 2023

In this paper, we show that for an isometry on a Banach space the analytic spectral subspace coincides with the algebraic spectral subspace. Using this result, we have the following result. Let T be a bounded linear operator with property (δ) on a Banach space X. And let S be an isometry on a Banach space Y . Then every generalized intertwining linear operator θ : X → Y for (S, T) is continuous if and only if the pair (S, T) has no critical eigenvalue.

• 대한수학회논문집
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• 제9권3호
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• pp.617-627
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• 1994

Algebraic spectral subspaces and admissible operators were introduced by K. B. Laursen and M. M. Neumann in 1988 [L88], [N]. These concepts are useful in automatic continuity problems of intertwining linear operators on Banach spaces. In this paper we characterize the algebraic spectral subspaces of generalized scalar operators. From this characterization we show that generalized scalar operators are admissible. Also we show that doubly power bounded operators are generalized scalar. And using the spectral capacity we show that a generalized scalar operator is decomposable. Then we give an example of an operator which is not admissible but decomposable.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1263-1272
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• 2008

Let T and S be bounded linear operators on Banach spaces X and y, respectively. A linear map A : X ${\rightarrow}$ y is said to be an intertwiner if AT - SA = 0. In this paper we study the relation between local spectral properties of T and S on the assumption of AT - SA = 0. We give some example of intertwiner with T and S.

• 충청수학회지
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• 제16권1호
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• pp.37-48
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• 2003

In this paper, we show that for a pure hyponormal operator the analytic spectral subspace and the algebraic spectral subspace are coincide. Using this result, we have the following result: Let T be a decomposable operator on a Banach space X and let S be a pure hyponormal operator on a Hilbert space H. Then every linear operator ${\theta}:X{\rightarrow}H$ with $S{\theta}={\theta}T$ is automatically continuous.

• 충청수학회지
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• 제29권4호
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• pp.677-686
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• 2016

Algebraic spectral subspaces were introduced by Johnson and Sinclair via a transnite sequence of spaces. Laursen simplified the definition of algebraic spectral subspace. Algebraic spectral subspaces are useful in automatic continuity theory of intertwining linear operators on Banach spaces. In this paper, we characterize algebraic spectral subspaces of operators with finite ascent. From this characterization we show that if T is a generalized scalar operator, then T has finite ascent.

• 대한수학회지
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• 제33권2호
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• pp.347-365
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• 1996

Let X and Y be Banach spaces and consider a linear operator $\theta : X \to Y$. The basic automatic continuity problem is to derive the continuity of $\theta$ from some prescribed algebraic conditions. For example, if $\theta : X \to Y$ is a linear operator intertwining with $T \in L(X)$ and $S \in L(Y)$, one may look for algebraic conditions on T and S which force $\theta$ to be continuous.

• 호남수학학술지
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• 제31권2호
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• pp.137-145
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• 2009

Let T ${\in}$ $\mathcal{L}$(X), S ${\in}$ $\mathcal{L}$(Y ), A ${\in}$ $\mathcal{L}$(X, Y ) and B ${\in}$ $\mathcal{L}$(Y,X) such that SA = AT, TB = BS, AB = S and BA = T. Then S and T shares that same local spectral properties SVEP, property (${\beta}$), property $({\beta})_{\epsilon}$, property (${\delta}$) and decomposability. From these common local spectral properties, we give some results related with Aluthge transforms and subscalar operators.