Operator space and Its application

众所周知，矩阵理论是应用数学领域的一个有用工具。我们使用术语“运算符”作为无限维空间中的矩阵。在算子理论中，出现了许多意想不到的现象，而这些现象在有限维空间中是不会出现的。在算子代数或算子理论中，关于某些范数收敛或不收敛的论证中，有时会出现这种现象。我们用积极性的概念来研究这些事实。算子单调函数是指在函数核心下保持算子序的函数，矩阵的单调性与算子的单调性等价。我们可以得到许多函数的算子单调性的特征。我们还得到了算子空间的广义Haagerup张量积的刻划。利用算子的Schur积，我们可以实现算子空间的结果.

It is well-known that the theory of matrices is a useful tool for the field of Applied Mathematics. We use the terminology "Operators" as Matrices in infinitely dimensional spaces. In the theory of operators, many unexpected phoenomena occur and such phoenomena do not occur in finitedimensional spaces. In the theory of Operator Algebra or Operators, such phoenomena sometimes occur in the argument in the convergence or not with respect to some norms. We study such facts using the notion of positivity. Operator monotone functions means functions which preserve the order of operators under functional cauculus and monotonicity for matrices is equivalent to that for Operators. We can get the characterization of operator monotonicity for many functions. We also get the characterization of extended Haagerup tensor product for Operator spaces. Using the Schur product of operators, we could realize the result for operator spaces.