Hilbert Space of Real Sequences
نویسندگان
چکیده
One can prove the following two propositions: (1) The carrier of l2-Space = the set of l2-real sequences and for every set x holds x is an element of the carrier of l2-Space iff x is a sequence of real numbers and idseq(x) idseq(x) is summable and for every set x holds x is a vector of l2-Space iff x is a sequence of real numbers and idseq(x) idseq(x) is summable and 0l2-Space = Zeroseq and for every vector u of l2-Space holds u = idseq(u) and for all vectors u, v of l2-Space holds u+v = idseq(u)+ idseq(v) and for every real number r and for every vector u of l2-Space holds r · u = r idseq(u) and for every vector u of l2-Space holds −u = −idseq(u) and idseq(−u) = −idseq(u) and for all vectors u, v of l2-Space holds u − v = idseq(u) − idseq(v) and for all vectors v, w of
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