• Journal of applied mathematics & informatics
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• 제8권1호
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• pp.97-109
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• 2001

This article is devoted to “forgotten” and rarely used technique of matrix analysis, introduced in 60-70th and enhanced by authors. We will study the matrix trace operator and it’s differentiability. This idea generalizes the notion of scalar derivative for matrix computations. The list of the most common derivatives is given at the end of the article. Additionally we point out a close connection of this technique with a least square problem in it’s classical and generalized case.

• 대한수학회보
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• 제39권1호
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• pp.63-69
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• 2002

Given vectors x and y in a Hilbert space, an intepolating operator is a bounded operator T such that Tx=y. an interpolating operator for n vectors satisfies the equation Tx$_{i}$=y, for i=1, 2,…, n. In this article, we obtained the fellowing : Let x = (x$_{i}$) and y = (y$_{i}$) be two vectors in H such that x$_{i}$$\neq$0 for all i = 1, 2,…. Then the following statements are equivalent. (1) There exists an operator A in AlgＬ such that Ax = y, A is a trace-class operator and every E in Ｌ reduces A. (2) (equation omitted).mitted).

• Korean Journal of Mathematics
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• 제24권2호
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• pp.273-296
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• 2016

Some new trace inequalities for convex functions of self-adjoint operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated. Some trace inequalities for matrices are also derived. Examples for the operator power and logarithm are presented as well.

• 대한수학회보
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• 제58권1호
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• pp.59-70
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• 2021

In this paper, we study two operator-valued inequalities for quantum Wigner-Yanase-Dyson skew information related to module operators. These are extended results of the trace inequalities for Wigner-Yanase-Dyson skew information. Moreover, we study a sufficient condition to prove an uncertainty relation for operator-valued generalized quantum Wigner-Yanase-Dyson skew information related to module operators and a pair of functions (f, g). Also, we obtain several previous results of scalar-valued cases as a consequence of our main result.

• 대한수학회지
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• 제33권2호
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• pp.309-318
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• 1996

The Gross Laplacian $\Delta_G$ was introduced by Groww for a function defined on an abstract Wiener space (H,B) [1,7]. Suppose $\varphi$ is a twice H-differentiable function defined on B such that $\varphi"(x)$ is a trace class operator of H for every x \in B.in B.

• East Asian mathematical journal
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• 제14권1호
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• pp.21-26
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• 1998

The Fulgede-Putnam theorem asserts as if A and Bare normal operators and X is an operator such that AX=XB, then A*X=XB*. In this paper, we show that if A is k-quasihyponormal and B* is invertible k-quasihyponormal such that AX=XB for a Hilbert-Schmidt operator X, then A*X=XB*.

• Journal of applied mathematics & informatics
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• 제41권1호
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• pp.123-132
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• 2023

We define an operator version of the relative Rényi entropy as the generalization of relative von Neumann entropy, and provide its fundamental properties and the bounds for its trace value. Moreover, we see an effect of the relative Rényi entropy under tensor product, and show the sub-additivity for density matrices.

• Kyungpook Mathematical Journal
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• 제63권1호
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• pp.105-122
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• 2023

We present explicit formulas for the spectra of higher spin operators on the subbundle of the bundle of spinor-valued trace free symmetric tensors that are annihilated by Clifford multiplication over the standard sphere in odd dimension. In the even dimensional case, we give the spectra of the square of such operators. The Dirac and Rarita-Schwinger operators are zero-form and one-form cases, respectively. We also give eigenvalue formulas for the conformally invariant differential operators of all odd orders on the subbundle of the bundle of spinor-valued forms that are annihilated by Clifford multiplication in both even and odd dimensions on the sphere.

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.979-982
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• 2022

This paper covers some important operator inequalities connected with traces of matrices, from the classical inequalities we obtained new inequalities connected with traces of matrices which are better than the others.

• 대한수학회논문집
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• 제16권4호
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• pp.621-626
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• 2001

Let { $A_{>o}$ t= exp(M log t)} $_{t}$ be a dilation group where M is a real n$\times$n matrix whose eigenvalues has strictly positive real part, and let $\rho$be an $A_{t}$ -homogeneous distance function defined on ( $R^{n}$ ). Suppose that K is a function defined on ( $R^{n}$ ) such that /K(x)/$\leq$ (No Abstract.see full/text) for a decreasing function defined on (t) on R+ satisfying where wo(x)=│log│log (x)ll. For f$\in$ $L_{1}$ ( $R^{n}$ ), define f(x)=sup t>0 Kt*f(x)=t-v K(Al/tx) and v is the trace of M. Then we show that \ulcorner is a bounded operator of $L_{-{1}( $R^{n}$ ) into $L^1$,$\infty$( $R^{n}$).