• Honam Mathematical Journal
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• v.8 no.1
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• pp.1-19
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• 1986

We show that a (possibly unbounded) linear operator, T, is scalar on the real line (spectral operator of scalar type, with real spectrum) if and only if (iT) generates a uniformly bounded semigroup and $(1-iT)(1+iT)^{-1}$ is scalar on the unit circle. T is scalar on [0, $\infty$) if and only if T generates a uniformly bounded semigroup and $(1+T)^{-1}$ is scalar on [0,1). By analogy with these results, we define $C^0$-scalar, on the real line, or [0. $\infty$), for an unbounded operator. We show that a generator of a positive-definite group is $C^0$-scalar on the real line. and a generator of a completely monotone semigroup is $C^0$-scalar on [0, $\infty$). We give sufficient conditions for a closed operator, T, to generate a positive-definite group: the sequence < $\phi(T^{n}x)$ > $_{n=0}^{\infty}$ must equal the moments of a positive measure on the real line, for sufficiently many positive $\phi$ in $X^{*}$, x in X. If the measures are supported on [0, $\infty$), then T generates a completely monotone semigroup. On a reflexive Banach lattice, these conditions are also necessary, and are equivalent to T being scalar, with positive projection-valued measure. T generates a completely monotone semigroup if and only if T is positive and m-dispersive and generates a bounded holomorphic semigroup.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.1043-1056
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• 2008

The spanning column rank of an $m{\times}n$ matrix A over a semiring is the minimal number of columns that span all columns of A. We characterize linear operators that preserve the sets of matrix ordered pairs which satisfy multiplicative properties with respect to spanning column rank of matrices over semirings.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.465-472
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• 2010

In this paper, we consider two extreme sets of zero-term rank sum of fuzzy matrix pairs: $$\cal{z}_1(\cal{F})=\{(X,Y){\in}\cal{M}_{m,n}(\cal{F})^2{\mid}z(X+Y)=min\{z(X),z(Y)\}\};$$ $$\cal{z}_2(\cal{F})=\{(X,Y){\in}\cal{M}_{m,n}(\cal{F})^2{\mid}z(X+Y)=0\}$$. We characterize the linear operators that preserve these two extreme sets of zero-term rank sum of fuzzy matrix pairs.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.113-123
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• 2014

The term rank of a matrix A over a semiring $\mathcal{S}$ is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we characterize linear operators that preserve the sets of matrix ordered pairs which satisfy extremal properties with respect to term rank inequalities of matrices over nonbinary Boolean semirings.

• Journal of the Korean Mathematical Society
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• v.40 no.6
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• pp.943-950
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• 2003

The maximal column rank of an m by n matrix A over max algebra is the maximal number of the columns of A which are linearly independent. We compare the maximal column rank with rank of matrices over max algebra. We also characterize the linear operators which preserve the maximal column rank of matrices over max algebra.

• 제어로봇시스템학회:학술대회논문집
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• 1988.10a
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• pp.169-171
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• 1988

This paper deals with the robustness property of Kalman filters for linear systems with delay in output. The operator-type Riccati equation is transformed to algebraic equations, and the circle condition is derived. Based on the circle condition, it is shown that the same nondivergence margin, (1/2, .inf.) gain margin and +-60.deg. phase margin, is guaranteed as for ordinary systems.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.271-283
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• 2018

In this paper, we introduce various first order (p, q)-difference equations. We investigate solutions to equations which are linear (p, q)-difference equations and nonlinear (p, q)-difference equations. We also find some properties of (p, q)-calculus, exponential functions, and inverse function.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.195-205
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• 2007

The maximal column rank of an $m{\times}n$ matrix A over the ring of integers, is the maximal number of the columns of A that are weakly independent. We characterize the linear operators that preserve the maximal column ranks of integer matrices.

• Journal of the Korean Mathematical Society
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• v.47 no.1
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• pp.71-81
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• 2010

We characterize linear operators that preserve sets of matrix ordered pairs which satisfy extreme cases with respect to maximal column rank inequalities of matrix multiplications over semirings.

• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.215-220
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• 1992

Using a matrix method, pp. Antosik and C. Swartz have obtained a series of nice properties of bounded multiplier convergent (BMC) series on metric linear spaces ([1],[8],[9]). In this paper, we establish a basic property of BMC series on topological vector spaces which is a generalization of a result due to J. Batt([2], Th.2). From this, we have obtained a kind of inclusion theorem of operator spaces. This theorem yields a nice result on infinite systems of linear equations.