The $n$-dual space of the space of $p$-summable sequences
نویسندگان
چکیده
منابع مشابه
ON THE SPACE OF p-SUMMABLE SEQUENCES
On the space l of p-summable sequences (of real numbers), one can derive a norm from the 2-norm as indicated by Gunawan [6]. The purpose of this note is to establish the equivalence between such a norm and the usual norm on l. We show that our result is useful in understanding the topology of l as a 2-normed space.
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We prove the (strong) equivalence between two known n-norms on the space l of p-summable sequences (of real numbers). The first n-norm is derived from Gähler’s formula [2], while the second is due to Gunawan [6]. The equivalence is proved by using the properties of the volume of ndimensional parallelepipeds in l.
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The subset the set of l1-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 l1-real sequences if and only if x ∈ the set of real sequences and idseq(x) is absolutely summable. Let us observe that the set of l1-real sequences is non empty. One can prove the following two propositions: (1) The set of l1-real sequ...
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ژورنال
عنوان ژورنال: Mathematica Bohemica
سال: 2013
ISSN: 0862-7959,2464-7136
DOI: 10.21136/mb.2013.143516