‎In this short note‎, ‎we present some inequalities for relative operator entropy which are generalizations of some results obtained by Zou [Operator inequalities associated with Tsallis relative operator entropy‎, ‎{em Math‎. ‎Inequal‎. ‎Appl.}‎ ‎{18} (2015)‎, ‎no‎. ‎2‎, ‎401--406]‎. ‎Meanwhile‎, ‎we also show some new lower and upper bounds for relative operator entropy and Tsallis relative o...

We introduce a new concept of unbounded solutions to the operator Riccati equation A1X − XA0 − XV X + V ∗ = 0 and give a complete description of its solutions associated with the spectral graph subspaces of the block operator matrix B = ( A0 V V ∗ A1 ) . We also provide a new characterization of the set of all contractive solutions under the assumption that the Riccati equation has a contractiv...

In this paper we use the explicit description of the Spin– 3 2 Dirac operator in real dimension 3 appeared in [17] to perform the algebraic analysis of the space of nullsolution of the system of equations given by several Rarita– Schwinger operators. We make use of the general theory provided by [10] and some standard Gröbner Bases techniques. Our aim is to show that such operator shares many o...

We nd the adjoint of the Askey-Wilson divided di erence operator with respect to the inner product on L 2 ( 1; 1; (1 x 2 ) 1=2 dx) de ned as a Cauchy principal value and show that the Askey-Wilson polynomials are solutions of a q-Sturm-Liouville problem. From these facts we deduce various properties of the polynomials in a simple and straightforward way. We also provide an operator theoretic de...

Abstract We prove that the half-BPS Wilson loop operator of N = 4 SYM in a symmetric representation of the gauge group has a bulk gravitational description in terms of a single D3-brane in AdS5×S, as argued in hep-th/0604007. We also show that a half-BPS Wilson loop operator in an arbitrary representation is described by the D3-brane configuration proposed in hep-th/0604007. This is demonstrate...

The performance of Genetic Algorithm (GA) depends on various operators. Crossover operator is one of them. Crossover operators are mainly classified as application dependent crossover operators and application independent crossover operators. Effect of crossover operators in GA is application as well as encoding dependent. This paper will help researchers in selecting appropriate crossover oper...