Advances in Operator Theory

Chandrodoy Chattopadhyay

Kalidas Mandal

Debmalya Sain

On the (m, n)-clock problem and the $$\ell _{\infty }-\ell _1$$ norm of a matrix

关于(m, n)-时钟问题与矩阵的$$\ell _{\infty }-\ell _1$$范数

Abstract This paper is devoted to matrices with hyperbolical Krein space numerical range. This shape characterizes the 2-by-2 case and persists for certain classes of matrices, independently of their size. Necessary and sufficient conditions for low dimensional tridiagonal matrices to have this shape are obtained involving only the matrix entries.

N. Bebiano

R. Lemos

G. Soares

Matrices with hyperbolical Krein space numerical range

具有双曲型Krein空间数值域的矩阵

Abstract Let X be a completely regular Hausdorff space and E and F be Banach spaces. Let $$C_{rc}(X,E)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>C</mml:mi> <mml:mrow> <mml:mi>rc</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi>E</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> denote the Banach space of all continuous functions $$f:X\rightarrow E$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>:</mml:mo> <mml:mi>X</mml:mi> <mml:mo>→</mml:mo> <mml:mi>E</mml:mi> </mml:mrow> </mml:math> such that f ( X ) is a relatively compact set in E , and $$\beta _\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>β</mml:mi> <mml:mi>σ</mml:mi> </mml:msub> </mml:math> be the strict topology on $$C_{rc}(X,E)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>C</mml:mi> <mml:mrow> <mml:mi>rc</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi>E</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . We characterize dominated and absolutely summing operators $$T:C_{rc}(X,E)\rightarrow F$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mo>:</mml:mo> <mml:msub> <mml:mi>C</mml:mi> <mml:mrow> <mml:mi>rc</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi>E</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>→</mml:mo> <mml:mi>F</mml:mi> </mml:mrow> </mml:math> in terms of their representing operator-valued Baire measures. It is shown that every absolutely summing $$(\beta _\sigma ,\Vert \cdot \Vert _F)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>β</mml:mi> <mml:mi>σ</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:mo>‖</mml:mo> <mml:mo>·</mml:mo> <mml:msub> <mml:mo>‖</mml:mo> <mml:mi>F</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -continuous operator $$T:C_{rc}(X,E)\rightarrow F$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mo>:</mml:mo> <mml:msub> <mml:mi>C</mml:mi> <mml:mrow> <mml:mi>rc</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi>E</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>→</mml:mo> <mml:mi>F</mml:mi> </mml:mrow> </mml:math> is dominated. Moreover, we obtain that every dominated operator $$T:C_{rc}(X,E)\rightarrow F$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mo>:</mml:mo> <mml:msub> <mml:mi>C</mml:mi> <mml:mrow> <mml:mi>rc</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi>E</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>→</mml:mo> <mml:mi>F</mml:mi> </mml:mrow> </mml:math> is absolutely summing if and only if every bounded linear operator $$U:E\rightarrow F$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>U</mml:mi> <mml:mo>:</mml:mo> <mml:mi>E</mml:mi> <mml:mo>→</mml:mo> <mml:mi>F</mml:mi> </mml:mrow> </mml:math> is absolutely summing.

Marian Nowak

Dominated and absolutely summing operators on the space $$\,C_{rc}(X,E)$$ of vector-valued continuous functions

支配算子和绝对求和算子在向量值连续函数空间$\,C_{rc}(X,E)$上的研究

Maninderjit Kaur

Isha Garg

Some singular value inequalities on commutators

一些交换子的奇异值不等式

Emil Prodan

Operator product states on tensor powers of $$C^*$$-algebras

张量幂上的算子乘积态在 $$C^*$$-代数中的应用

Abstract We investigate how continuous linear functionals can be represented in terms of generic operators and certain kernels (Peano kernels), and we study lower bounds for the operators as a consequence, in the space of square-integrable functions. We apply and develop the theory for the Riemann–Liouville fractional derivative (an inverse of the Riemann–Liouville integral), where inequalities are derived with the Gaussian hypergeometric function. This work is inspired by the recent contributions by Fernandez and Buranay (J Comput Appl Math 441:115705, 2024) and Jornet (Arch Math, 2024).

Marc Jornet

Juan J. Nieto

Representation and inequalities involving continuous linear functionals and fractional derivatives

连续线性泛函与分数阶导数的表示与不等式

短名	Adv. Oper. Theory.
Journal Impact	0.60
国际分区	MATHEMATICS(Q2)

ISSN	2538-225X, 2662-2009
h-index	16

涉及主题	数学纯数学数学分析物理量子力学计算机科学离散数学生物组合数学化学哲学遗传学几何学生物化学基因操作员（生物学）转录因子抑制因子基因表达语言学域代数上的巴拿赫空间认识论程序设计语言有界函数操作系统
出版信息	出版商: Tusi Mathematical Research Group (TMRG)，出版周期: ，期刊类型: journal，开源期刊: 否
基本数据	创刊年份: 2016，原创研究文献占比: 100.00%，自引率:12.50%， Gold OA占比: 6.70%

Advances in Operator Theory

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On the (m, n)-clock problem and the $$\ell _{\infty }-\ell _1$$ norm of a matrix

Matrices with hyperbolical Krein space numerical range

Dominated and absolutely summing operators on the space $$\,C_{rc}(X,E)$$ of vector-valued continuous functions

Some singular value inequalities on commutators

Operator product states on tensor powers of $$C^*$$-algebras

On the (m, n)-clock problem and the $$\ell _{\infty }-\ell _1$$ norm of a matrix

Matrices with hyperbolical Krein space numerical range

Some singular value inequalities on commutators

Dominated and absolutely summing operators on the space $$\,C_{rc}(X,E)$$ of vector-valued continuous functions

Representation and inequalities involving continuous linear functionals and fractional derivatives