Search Results - "UCHIYAMA, Mitsuru"
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Operator means and matrix quadratic equations
Published in Linear algebra and its applications (15-01-2021)“…Let A,B be N×N matrices such that A≥B≥0. We show that the matrix equation A=X+Y2, B=X#Y, 0≤X≤Y has a unique solution X=A−(A−B)#(A+B), Y=A+(A−B)#(A+B), where…”
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OPERATOR MONOTONE FUNCTIONS, POSITIVE DEFINITE KERNELS AND MAJORIZATION
Published in Proceedings of the American Mathematical Society (01-11-2010)“…Let f(t) be a real continuous function on an interval, and consider the operator function f(X) defined for Hermitian operators X. We will show that if f(X) is…”
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3
The principal inverse of the gamma function
Published in Proceedings of the American Mathematical Society (01-04-2012)“…Let \Gamma(x) the maximal zero of \Gamma'(x) \Gamma (x)\vert _{(\alpha, \infty)} \Gamma ^{-1}(x) \Gamma ^{-1}(x) \Gamma ^{-1}(z) {\bf C}\setminus (-\infty,…”
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4
Majorization and some operator monotone functions
Published in Linear algebra and its applications (01-04-2010)“…Let h ( t ) be a non-decreasing function on I and k ( t ) an increasing function on J . Then h is said to be majorized by k if k ( A ) ≦ k ( B ) implies h ( A…”
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Journal Article Conference Proceeding -
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A matrix subadditivity inequality for f( A + B) and f( A) + f( B)
Published in Linear algebra and its applications (01-06-2007)“…In 1999 Ando and Zhan proved a subadditivity inequality for operator concave functions. We extend it to all concave functions: Given positive semidefinite…”
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Subadditivity of eigenvalue sums
Published in Proceedings of the American Mathematical Society (01-05-2006)“…Let f(t) be a nonnegative concave function on 0 \leq t <\infty with f(0)=0, and let X, Y be n\times n matrices. Then it is known that \Vert f(|X+Y|)\Vert_1\leq…”
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A new majorization between functions, polynomials, and operator inequalities
Published in Journal of functional analysis (01-02-2006)“…Let P + be the set of all non-negative operator monotone functions defined on [ 0 , ∞ ) , and put P + - 1 = { h : h - 1 ∈ P + } . Then P + · P + - 1 ⊂ P + - 1…”
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Positive linear maps on C⁎-algebras and rigid functions
Published in Journal of mathematical analysis and applications (15-05-2017)“…Let a linear map Φ between two unital C⁎-algebras be positive and unital. Kadison showed that if f(t)=|t| and Φ(f(X))=f(Φ(X)) for all selfadjoint operators X,…”
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Inverse functions of polynomials and orthogonal polynomials as operator monotone functions
Published in Transactions of the American Mathematical Society (01-10-2003)“…We study the operator monotonicity of the inverse of every polynomial with a positive leading coefficient. Let \{p_n\}_{n=0}^{\infty } be a sequence of…”
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Operator Monotone Functions which Are Defined Implicitly and Operator Inequalities
Published in Journal of functional analysis (20-08-2000)“…The function tα (0<α<1) is operator monotone on 0⩽t<∞. This is known as the Löwner–Heinz inequality. However, not too many examples of concrete operator…”
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Operator monotone functions, Jacobi operators and orthogonal polynomials
Published in Journal of mathematical analysis and applications (15-05-2013)“…We reveal a connection between operator monotone functions and orthogonal polynomials. Especially, we express an operator monotone function with a Jacobi…”
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Operator inequalities: From a general theorem to concrete inequalities
Published in Linear algebra and its applications (15-01-2015)“…The aim of this paper is to give a method to extract concrete inequalities from a general theorem, which is established by making use of majorization relation…”
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Further extension of the Heinz-Kato-Furuta inequality
Published in Proceedings of the American Mathematical Society (01-10-1999)“…Let T be a bounded operator on a Hilbert space \mathfrak{H}, and A,B positive definite operators. Kato has shown that if \Vert T x \Vert \leq \Vert A x \Vert…”
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14
A converse of Loewner–Heinz inequality and applications to operator means
Published in Journal of mathematical analysis and applications (01-05-2014)“…Let f(t) be an operator monotone function. Then A⩽B implies f(A)⩽f(B), but the converse implication is not true. Let A♯B be the geometric mean of A,B⩾0. If…”
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An operator inequality related to Jensen's inequality
Published in Proceedings of the American Mathematical Society (01-11-2001)“…For bounded non-negative operators A and B, Furuta showed \[ 0\leq A \leq B {\rm implies } A^{\frac{r}{2}}B^sA^{\frac{r}{2}} \leq (A^{\frac{r}{2}}B^t…”
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Curvatures and Similarity of Operators with Holomorphic Eigenvectors
Published in Transactions of the American Mathematical Society (1990)“…The curvature of the holomorphic vector bundle generated by eigenvectors of operators is estimated, and the necessary and sufficient conditions for…”
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Regulatory status of excipients in Japan
Published in Drug information journal (1999)Get full text
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Some Sulfur-Containing Metabolites of Tri-n-butyltin Chloride in Male Rats
Published in Journal of agricultural and food chemistry (01-11-1999)“…In an attempt to elucidate metabolic destination of TBTO, sulfur-containing metabolites were investigated in the urine. Tri-n-butyltin chloride (TBTC),…”
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Superadditivity and derivative of operator functions
Published in Linear algebra and its applications (15-01-2015)“…We will show that if ∑i≠jAiAj≥0 for bounded operators Ai≥0 (i=1,2,⋯,n), then g(∑iAi)≥∑ig(Ai) for every operator convex function g(t) on [0,∞) with g(0)≤0; in…”
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Chemical Species of Organotin Compounds in Sediment at a Marina
Published in Journal of agricultural and food chemistry (01-09-1999)“…A bottom sediment collected in a marina was analyzed for organotin species, and >20 organotin compounds including biodegraded ones were confirmed by comparison…”
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