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Sequence spaces defined by a modulus. (English) Zbl 0631.46010
f: [0,\(\infty)\to [0,\infty)\) is called a modulus if (i) \(f(x)=0\) iff \(x=0\), (ii) \(f(x+y)\leq f(x)+f(y)\) for x,y\(\geq 0\), (iii) f is increasing, (iv) f is continuous.
Using the modulus f, the author introduces and studies three sequence spaces \(w_ 0(f)\), w(f), \(w_{\infty}(f)\) which generalizes the spaces \(w_ 0\), w, \(w_{\infty}\) of strongly summable sequences. Besides other results, it is shown that \(w_ 0(f)\) and w(f) are paranormed FK spaces.
Reviewer: C.Zălinescu

MSC:
46A45 Sequence spaces (including Köthe sequence spaces)
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