Search Results - "UCHIYAMA, Mitsuru"

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  1. 1

    Operator means and matrix quadratic equations by Uchiyama, Mitsuru

    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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    Journal Article
  2. 2

    OPERATOR MONOTONE FUNCTIONS, POSITIVE DEFINITE KERNELS AND MAJORIZATION by UCHIYAMA, MITSURU

    “…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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    Journal Article
  3. 3

    The principal inverse of the gamma function by UCHIYAMA, MITSURU

    “…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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    Journal Article
  4. 4

    Majorization and some operator monotone functions by Uchiyama, Mitsuru

    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
  5. 5

    A matrix subadditivity inequality for f( A + B) and f( A) + f( B) by Bourin, Jean-Christophe, Uchiyama, Mitsuru

    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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    Journal Article
  6. 6

    Subadditivity of eigenvalue sums by Uchiyama, Mitsuru

    “…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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    Journal Article
  7. 7

    A new majorization between functions, polynomials, and operator inequalities by Uchiyama, Mitsuru

    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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    Journal Article
  8. 8

    Positive linear maps on C⁎-algebras and rigid functions by Uchiyama, Mitsuru

    “…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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    Journal Article
  9. 9

    Inverse functions of polynomials and orthogonal polynomials as operator monotone functions by Uchiyama, Mitsuru

    “…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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    Journal Article
  10. 10

    Operator Monotone Functions which Are Defined Implicitly and Operator Inequalities by Uchiyama, Mitsuru

    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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    Journal Article
  11. 11

    Operator monotone functions, Jacobi operators and orthogonal polynomials by Uchiyama, Mitsuru

    “…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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    Journal Article
  12. 12

    Operator inequalities: From a general theorem to concrete inequalities by Uchiyama, Mitsuru

    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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    Journal Article
  13. 13

    Further extension of the Heinz-Kato-Furuta inequality by Uchiyama, Mitsuru

    “…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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    Journal Article
  14. 14

    A converse of Loewner–Heinz inequality and applications to operator means by Uchiyama, Mitsuru, Yamazaki, Takeaki

    “…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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    Journal Article
  15. 15

    An operator inequality related to Jensen's inequality by Uchiyama, Mitsuru

    “…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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    Journal Article
  16. 16

    Curvatures and Similarity of Operators with Holomorphic Eigenvectors by Uchiyama, Mitsuru

    “…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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    Journal Article
  17. 17

    Regulatory status of excipients in Japan by UCHIYAMA, M

    Published in Drug information journal (1999)
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    Conference Proceeding Journal Article
  18. 18

    Some Sulfur-Containing Metabolites of Tri-n-butyltin Chloride in Male Rats by Suzuki, Takashi, Kondo, Kazunari, Uchiyama, Mitsuru, Murayama, Mitsunori

    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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    Journal Article
  19. 19

    Superadditivity and derivative of operator functions by Uchiyama, Mitsuru, Uchiyama, Atsushi, Giga, Mariko

    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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    Journal Article
  20. 20

    Chemical Species of Organotin Compounds in Sediment at a Marina by Suzuki, Takashi, Kondo, Kazunari, Uchiyama, Mitsuru, Murayama, Mitsunori

    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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    Journal Article