Sequence spaces defined by a modulus. (English) Zbl 0631.46010

Maddox, Ivor J.

Math. Proc. Camb. Philos. Soc. 100, 161-166 (1986).

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)

Keywords:

modulus; sequence spaces; paranormed FK spaces

References:

[1]	DOI: 10.1112/blms/13.4.301 · Zbl 0445.46007
[2]	Ruckle, Canad. J. Math. 25 pp 973– (1973) · Zbl 0267.46008
[3]	Kuttner, J. London Math. Soc. 21 pp 118– (1946)
[4]	DOI: 10.1112/jlms/s1-43.1.285 · Zbl 0155.38802
[5]	Maddox, Math. Proc. Cambridge Philos. Soc. 95 pp 467– (1984)