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