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Tensorial and Hadamard Product Inequalities for Synchronous Functions

Yıl 2023, Cilt: 6 Sayı: 4, 177 - 187, 25.12.2023
https://doi.org/10.33434/cams.1362694

Öz

Let $H$ be a Hilbert space. In this paper we show among others that, if $f,$ $g$ are synchronous and continuous on $I$ and $A,$ $B$ are selfadjoint with spectra ${Sp}\left( A\right) ,$ ${Sp}\left( B\right) \subset I,$ then%
\begin{equation*}
\left( f\left( A\right) g\left( A\right) \right) \otimes 1+1\otimes \left(
f\left( B\right) g\left( B\right) \right) \geq f\left( A\right) \otimes
g\left( B\right) +g\left( A\right) \otimes f\left( B\right)
\end{equation*}%
and the inequality for Hadamard product%
\begin{equation*}
\left( f\left( A\right) g\left( A\right) +f\left( B\right) g\left( B\right)
\right) \circ 1\geq f\left( A\right) \circ g\left( B\right) +f\left(
B\right) \circ g\left( A\right) .
\end{equation*}%
Let either $p,q\in \left( 0,\infty \right) $ or $p,q\in \left( -\infty
,0\right) $. If $A,$ $B>0,$ then
\begin{equation*}
A^{p+q}\otimes 1+1\otimes B^{p+q}\geq A^{p}\otimes B^{q}+A^{q}\otimes B^{p},
\end{equation*}%
and%
\begin{equation*}
\left( A^{p+q}+B^{p+q}\right) \circ 1\geq A^{p}\circ B^{q}+A^{q}\circ B^{p}.
\end{equation*}

Kaynakça

  • [1] H. Araki, F. Hansen, Jensen’s operator inequality for functions of several variables, Proc. Amer. Math. Soc., 128 (7) (2000), 2075-2084.
  • [2] A. Koranyi, On some classes of analytic functions of several variables, Trans. Amer. Math. Soc., 101 (1961), 520-554.
  • [3] T. Furuta, J. Micic Hot, J. Pecaric, Y. Seo, Mond-Peˇcari´c Method in Operator Inequalities. Inequalities for Bounded Selfadjoint Operators on a Hilbert Space, Element, Zagreb, 2005.
  • [4] S. Wada, On some refinement of the Cauchy-Schwarz inequality, Lin. Alg. & Appl., 420 (2007), 433-440.
  • [5] J. I. Fujii, The Marcus-Khan theorem for Hilbert space operators, Math. Jpn., 41 (1995), 531-535.
  • [6] T. Ando, Concavity of certain maps on positive definite matrices and applications to Hadamard products, Lin. Alg. & Appl., 26 (1979), 203-241.
  • [7] J. S. Aujila, H. L. Vasudeva, Inequalities involving Hadamard product and operator means, Math. Japon., 42 (1995), 265-272.
  • [8] K. Kitamura, Y. Seo, Operator inequalities on Hadamard product associated with Kadison’s Schwarz inequalities, Scient. Math. 1(2) (1998), 237-241.
  • [9] P. Bhunia, K. Paul, A. Sen, Numerical radius inequalities for tensor product of operators, Proc. Indian Acad. Sci. (Math. Sci.), 133(3) (2023).
  • [10] H. L. Gau, K. Z. Wang, P. Y. Wu, Numerical radii for tensor products of operators, Integr. Equ. Oper. Theory, 78 (2014), 375–382.
Yıl 2023, Cilt: 6 Sayı: 4, 177 - 187, 25.12.2023
https://doi.org/10.33434/cams.1362694

Öz

Kaynakça

  • [1] H. Araki, F. Hansen, Jensen’s operator inequality for functions of several variables, Proc. Amer. Math. Soc., 128 (7) (2000), 2075-2084.
  • [2] A. Koranyi, On some classes of analytic functions of several variables, Trans. Amer. Math. Soc., 101 (1961), 520-554.
  • [3] T. Furuta, J. Micic Hot, J. Pecaric, Y. Seo, Mond-Peˇcari´c Method in Operator Inequalities. Inequalities for Bounded Selfadjoint Operators on a Hilbert Space, Element, Zagreb, 2005.
  • [4] S. Wada, On some refinement of the Cauchy-Schwarz inequality, Lin. Alg. & Appl., 420 (2007), 433-440.
  • [5] J. I. Fujii, The Marcus-Khan theorem for Hilbert space operators, Math. Jpn., 41 (1995), 531-535.
  • [6] T. Ando, Concavity of certain maps on positive definite matrices and applications to Hadamard products, Lin. Alg. & Appl., 26 (1979), 203-241.
  • [7] J. S. Aujila, H. L. Vasudeva, Inequalities involving Hadamard product and operator means, Math. Japon., 42 (1995), 265-272.
  • [8] K. Kitamura, Y. Seo, Operator inequalities on Hadamard product associated with Kadison’s Schwarz inequalities, Scient. Math. 1(2) (1998), 237-241.
  • [9] P. Bhunia, K. Paul, A. Sen, Numerical radius inequalities for tensor product of operators, Proc. Indian Acad. Sci. (Math. Sci.), 133(3) (2023).
  • [10] H. L. Gau, K. Z. Wang, P. Y. Wu, Numerical radii for tensor products of operators, Integr. Equ. Oper. Theory, 78 (2014), 375–382.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Temel Matematik (Diğer)
Bölüm Makaleler
Yazarlar

Sever Dragomır 0000-0003-2902-6805

Erken Görünüm Tarihi 7 Kasım 2023
Yayımlanma Tarihi 25 Aralık 2023
Gönderilme Tarihi 19 Eylül 2023
Kabul Tarihi 31 Ekim 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 6 Sayı: 4

Kaynak Göster

APA Dragomır, S. (2023). Tensorial and Hadamard Product Inequalities for Synchronous Functions. Communications in Advanced Mathematical Sciences, 6(4), 177-187. https://doi.org/10.33434/cams.1362694
AMA Dragomır S. Tensorial and Hadamard Product Inequalities for Synchronous Functions. Communications in Advanced Mathematical Sciences. Aralık 2023;6(4):177-187. doi:10.33434/cams.1362694
Chicago Dragomır, Sever. “Tensorial and Hadamard Product Inequalities for Synchronous Functions”. Communications in Advanced Mathematical Sciences 6, sy. 4 (Aralık 2023): 177-87. https://doi.org/10.33434/cams.1362694.
EndNote Dragomır S (01 Aralık 2023) Tensorial and Hadamard Product Inequalities for Synchronous Functions. Communications in Advanced Mathematical Sciences 6 4 177–187.
IEEE S. Dragomır, “Tensorial and Hadamard Product Inequalities for Synchronous Functions”, Communications in Advanced Mathematical Sciences, c. 6, sy. 4, ss. 177–187, 2023, doi: 10.33434/cams.1362694.
ISNAD Dragomır, Sever. “Tensorial and Hadamard Product Inequalities for Synchronous Functions”. Communications in Advanced Mathematical Sciences 6/4 (Aralık 2023), 177-187. https://doi.org/10.33434/cams.1362694.
JAMA Dragomır S. Tensorial and Hadamard Product Inequalities for Synchronous Functions. Communications in Advanced Mathematical Sciences. 2023;6:177–187.
MLA Dragomır, Sever. “Tensorial and Hadamard Product Inequalities for Synchronous Functions”. Communications in Advanced Mathematical Sciences, c. 6, sy. 4, 2023, ss. 177-8, doi:10.33434/cams.1362694.
Vancouver Dragomır S. Tensorial and Hadamard Product Inequalities for Synchronous Functions. Communications in Advanced Mathematical Sciences. 2023;6(4):177-8.

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