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 [: R, Y :] into Y , let a be a real number, and let f be a function from X into Y . Then F ◦(a, f) is an element of Y X . One can prove the following propositions: (1) Let X be a non empty set and Y be a non empty loop structure. Then there exists a binary operation A1 on (the carrier of Y ) X such that for all elements f , g of (the carrier of Y ) holds A1(f, g) = (the addition of Y )◦(f, g). (2) Let X be a non empty set and Y be a real linear space. Then there exists a function M1 from [: R, (the carrier of Y ) X :] into (the carrier of Y ) such that for every real number r and for every element f of (the carrier of Y ) and for every element s of X holds M1(〈r, f〉)(s) = r · f(s).
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