Complex Banach Space of Bounded Linear Operators
Complex Banach Space of Bounded Linear Operators
复制标题
有界线性算子的复Banach空间
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
N. Endou
中科院分区：
文献类型：
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作者：
N. Endou
设X是一个集合，Y是一个非空集，F是一个从[：C，Y：]到Y的函数，c是一个复数，f是一个从X到Y的函数。则F ∈（c，f）是Y X的元素。我们现在陈述命题（1）令X是非空集，Y是复线性空间。则存在一个从[：C，（Y的载体）X：]到（Y的载体）的函数M1，使得对于每个复形c和对于（Y的载体）的每个元素f和对于X的每个元素s，保持M1（c，f）（s）= c · f（s）。设X是一个非空集，Y是一个复线性空间。函子FuncExtMult（X，Y）产生一个从[：C，（Y的载体）：]到（Y的载体）的函数，并由条件（定义1）定义。(Def. 1）设c是复形，f是（Y的载体）的元素，x是X的元素。则（FuncExtMult（X，Y））（f ∈ c，f ∈）（x）= c · f（x）。
Let X be a set, let Y be a non empty set, let F be a function from [: C, Y :] into Y , let c be a complex number, and let f be a function from X into Y . Then F ◦(c, f) is an element of Y X . We now state the proposition (1) Let X be a non empty set and Y be a complex linear space. Then there exists a function M1 from [: C, (the carrier of Y ) X :] into (the carrier of Y ) such that for every Complex c and for every element f of (the carrier of Y ) and for every element s of X holds M1(〈c, f〉)(s) = c · f(s). Let X be a non empty set and let Y be a complex linear space. The functor FuncExtMult(X, Y ) yields a function from [: C, (the carrier of Y ) :] into (the carrier of Y ) and is defined by the condition (Def. 1). (Def. 1) Let c be a Complex, f be an element of (the carrier of Y ) , and x be an element of X. Then (FuncExtMult(X,Y ))(〈c, f〉)(x) = c · f(x).