Tusi Mathematical Research Group (TMRG) Advances in Operator Theory 2538-225X 1 1 2016 12 01 Square inequality and strong order relation 1 7 38442 10.22034/aot.1610.1035 EN Tsuyoshi Ando Journal Article 2016 10 23 It is well-known that for Hilbert space linear operators \$0 leq A\$ and \$0 leq C\$, inequality<br />\$C leq A\$ does not imply \$C^2 leq A^2.\$ We introduce a strong order relation \$0 leq B lll A\$, which guarantees that \$C^2 leq B^{1/2}AB^{1/2} text{for all} 0 leq C leq B,\$ and that \$C^2 leq A^2\$ when \$B\$ commutes with \$A\$. Connections of this approach with the arithmetic-geometric mean inequality of Bhatia--Kittaneh as well as the Kantorovich constant of \$A\$ are mentioned. http://www.aot-math.org/article_38442_d9989f3fd74949a9277c13928345bcef.pdf
Tusi Mathematical Research Group (TMRG) Advances in Operator Theory 2538-225X 1 1 2016 12 01 Operators reversing orthogonality in normed spaces 8 14 38478 10.22034/aot.1610.1021 EN Jacek Chmielinski Pedagogical University of Cracow Journal Article 2016 10 02 We consider linear operators \$Tcolon Xto X\$ on a normed space \$X\$ which reverse orthogonality, i.e., satisfy the condition<br />\$\$<br />xbot yquad Longrightarrowquad Tybot Tx,qquad x,yin X,<br />\$\$<br />where \$bot\$ stands for Birkhoff orthogonality. http://www.aot-math.org/article_38478_7c15ca13cf82bd7c234123b9bb787e61.pdf
Tusi Mathematical Research Group (TMRG) Advances in Operator Theory 2538-225X 1 1 2016 12 01 Recent developments of Schwarz's type trace inequalities for operators in Hilbert spaces 15 91 38906 10.22034/aot.1610.1032 EN Sever Dragomir Journal Article 2016 10 13 In this paper, we survey some recent trace inequalities for operators in<br />Hilbert spaces that are connected to Schwarz's, Buzano's and Kato's<br />inequalities and the reverses of Schwarz inequality known in the literature<br />as Cassels' inequality and Shisha--Mond's inequality. Applications for some<br />functionals that are naturally associated to some of these inequalities and<br />for functions of operators defined by power series are given. Examples for<br />fundamental functions such as the power, logarithmic, resolvent and<br />exponential functions are provided as well. http://www.aot-math.org/article_38906_2284ce53f9a52e67a0bd59db77882ece.pdf
Tusi Mathematical Research Group (TMRG) Advances in Operator Theory 2538-225X 1 1 2016 12 01 Fixed points of contractions and cyclic contractions on \$C^{*}\$-algebra-valued \$b\$-metric spaces 92 103 38953 10.22034/aot.1610.1030 EN Zoran Kadelburg Antonella Nastasi Department of Mathematics and Computer Science, University of Palermo Stojan Radenovic Faculty of Mechanical Engineering, University of Belgrade Pasquale Vetro Department of Mathematics and Computer Science, University of Palermo Journal Article 2016 10 13 In this paper, we discuss and improve some recent results about<br />contractive and cyclic mappings established in the framework of<br />\$C^{*}\$-algebra-valued \$b\$-metric spaces. Our proofs are much<br />shorter than the ones in existing literature. Also, we give two<br />examples that support our approach. http://www.aot-math.org/article_38953_c05393d482953043bf82592dbe9115d3.pdf
Tusi Mathematical Research Group (TMRG) Advances in Operator Theory 2538-225X 1 1 2016 12 01 Strengthened converses of the Jensen and Edmundson-Lah-Ribaric inequalities 104 122 39602 10.22034/aot.1610.1040 EN Mario Krnic Rozarija Mikic Josip Pecaric Journal Article 2016 10 28 In this paper, we give converses of the Jensen and Edmundson-Lah-Ribaric inequalities which are more accurate than the existing ones. These converses are given in a difference form and they rely on the recent refinement of the Jensen inequality obtained via linear interpolation of a convex function.<br /> As an application, we also derive improved converse relations for generalized means, for the Holder and Hermite-Hadamard inequalities as well as for the inequalities of Giaccardi and Petrovic. http://www.aot-math.org/article_39602_68b5a4686f6f70886b4597b3324fecf9.pdf
Tusi Mathematical Research Group (TMRG) Advances in Operator Theory 2538-225X 1 1 2016 12 01 Positive definite kernels and boundary spaces 123 133 40547 10.22034/aot.1610.1044 EN Feng Tian Palle Jorgensen Journal Article 2016 10 29 We consider a kernel based harmonic analysis of "boundary,"<br />and boundary representations. Our setting is general: certain classes<br />of positive definite kernels. Our theorems extend (and are motivated<br />by) results and notions from classical harmonic analysis on the disk.<br />Our positive definite kernels include those defined on infinite discrete<br />sets, for example sets of vertices in electrical networks, or discrete<br />sets which arise from sampling operations performed on positive definite<br />kernels in a continuous setting. <br /><br />Below we give a summary of main conclusions in the paper: Starting<br />with a given positive definite kernel \$K\$ we make precise generalized<br />boundaries for \$K\$. They are measure theoretic "boundaries."<br />Using the theory of Gaussian processes, we show that there is always<br />such a generalized boundary for any positive definite kernel. http://www.aot-math.org/article_40547_eff3ba46ba5c59cdb0769db9b537f59e.pdf
Tusi Mathematical Research Group (TMRG) Advances in Operator Theory 2538-225X 1 1 2016 12 01 (p,q)-type beta functions of second kind 134 146 40548 10.22034/aot.1609.1011 EN Ali Aral Vijay Gupta No Journal Article 2016 10 17 In the present article, we propose the (p,q)-variant of beta function of second kind and establish a relation between the generalized beta and gamma functions using some identities of the post-quantum calculus. As an application, we also propose the (p,q)-Baskakov-Durrmeyer operators, estimate moments and establish some direct results. http://www.aot-math.org/article_40548_62e3853082d62ca9f3f5adb1dcc194c2.pdf