Complex Banach Space of Bounded Linear Operators
نویسنده
چکیده
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).
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