Examples of using 算子 in Chinese and their translations into English
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因此，算子的谱总是包含其所有特征值，但却不限于此。
Thus the spectrum of an operator always contains all its eigenvalues, but is not limited to them.因此，如果A和B是两个希尔伯特-施密特算子，希尔伯特-施密特内积可以如下定义.
Therefore, if A and B are two 在数学中，一个希尔伯特-施密特算子（得名于大卫·希尔伯特和埃哈德·施密特）,是希尔伯特空间H上的有界算子A，有有限的希尔伯特-施密特范数.
可以将某些类的有界算子视为经典序列空间的非交换类比，利用迹类算子作为序列空间l1(N)的非交换类比。
尖括号⟨⋅,⋅⟩{\displaystyle\langle\cdot,\cdot\rangle}是希尔伯特空间上的标量积;右边的和依算子范数收敛。
The bracket⟨⋅,⋅⟩{\displaystyle\langle\cdot,\cdot\rangle} is the scalar product on the Hilbert space; the sum on the right hand side converges in the operator norm.两个希尔伯特-施密特算子的乘积有有限的迹类范数；因此，如果A和B是两个希尔伯特-施密特算子，希尔伯特-施密特内积可以如下定义.
The product of two Hilbert- Schmidt operators has finite trace class norm; therefore, if A and B are two Hilbert- Schmidt operators, the Hilbert- Schmidt inner product can be defined as.线性算子是最常见的算子。设U和V是域K上的向量空间。算子A：U→V被称为线性，如果.
The most common kind of operator encountered are linear 索林·特奥多尔·波帕(英文:SorinTeodorPopa)(生日：1953年3月24日)是一位罗马尼亚裔美籍数学家，主要研究算子代数。波帕现任加州大学洛杉矶分校教授。[1].
Sorin Teodor Popa(24 March 1953) is a Romanian-American mathematician working on operator algebras. He is a professor at UCLA.[1].这项工作显示了S4和S5是内部代数的模型，它是最初设计用来捕获拓扑学的内部算子和闭包算子的性质的布尔代数的真扩展。
This work revealed that S4 and S5 are models of interior algebra, a proper extension of Boolean algebra originally designed to capture the properties of the interior and closure operators of topology.空间Z(Σ)是量子理论的希尔伯特空间，而带有哈密顿算符H的物理理论将具有时间演化算子eitH或“虚构时间”算子e-tH。
The space Z(M) is the Hilbert space of the quantum theory and a physical theory, with a Hamiltonian H, will have a time evolution operator eitH or an"imaginary time" operator e- tH.时间逻辑，在1957年由A.N.Prior发明，与模态逻辑有密切的关联，因为增加了模态算子和，分别意味着今后和至今，导致了时间逻辑的一个系统。
Prior created modern temporal logic, closely related to modal logic, in 1957 by adding modal operators and meaning"eventually" and"previously".他用表示函数χ(y)简写ψ(x,y):无界μ算子--函数μy--经常定义于教科书中。
He designated the representing functions χ(y) rather than ψ( x, y): The unbounded μ operator- the function μy- is the one commonly defined in the texts.函数f{\displaystylef}是算子凹的如果-f{\displaystyle-f}是算子凸的，即上面关于f{\displaystylef}不等式符号反过来成立。
A function f{\displaystyle f} is operator concave if- f{\displaystyle-f} is operator convex, i.e. the inequality above for f{\displaystyle f} is reversed.它们算子加法下不是向量空间，例如，id和-id都是可逆的（双射），但它们的和为0，不可逆。
They do not form a vector space under the addition of operators, e.g. both id and-id are invertible(bijective), but their sum, 0, is not.对于-1≤p≤0{\displaystyle-1\leqp\leq0}，{\displaystylef（t）=-t^{p}}</img>是算子单调和算子凹。
For- 1≤ p≤ 0{\displaystyle -1\leq p\leq 0}, the function f( t)=- t p{\displaystyle f( t)=- t^{ p}} is operator monotone and operator concave.在数学里面，有很多关于希尔伯特空间上的矩阵和线性算子的不等式。本文主要论述和矩阵的迹有关的一些重要的算子不等式。[1][2][3][4].
In mathematics, there are many kinds of inequalities involving matrices and linear operators on Hilbert spaces. This article covers some important operator inequalities connected with traces of matrices.[ 1][ 2][ 3][ 4].算子单调.
Operator monotone.线性算子.
Linear operators.无损算子.
NDT Operator.全连续算子.
Completely continuous operators.
