Banach Space of Bounded Real Sequences
نویسنده
چکیده
The subset the set of bounded real sequences of the linear space of real sequences is defined by the condition (Def. 1). (Def. 1) Let x be a set. Then x ∈ the set of bounded real sequences if and only if x ∈ the set of real sequences and idseq(x) is bounded. Let us note that the set of bounded real sequences is non empty and the set of bounded real sequences is linearly closed. One can prove the following proposition (1) 〈the set of bounded real sequences, Zero (the set of bounded real sequences, the linear space of real sequences), Add (the set of bounded real sequences, the linear space of real sequences), Mult (the set of bounded real sequences, the linear space of real sequences)〉 is a subspace of the linear space of real sequences. One can verify that 〈the set of bounded real sequences, Zero (the set of bounded real sequences, the linear space of real sequences), Add (the set of bounded
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