Boundedness of superposition operators on some sequence spaces defined by moduli

• Autorzy: Molder A.
• Języki publikacji: EN

Abstrakty

EN

For a solid sequence space lambda and a sequence of modulus functions fi = (phik) let lambda(fi) = {x = (xk) : (phik(|xk|)) is an element of lambda}. Provided another solid sequence space ž and a sequence of modulus functions psi= psi(k), we give necessary and sufficient conditions for the local boundedness and boundedness of superposition operators Pf from lambda(fi)) into ž(psi) for some Banach sequence spaces lambda and ž under the assumptions that topologies on the sequence spaces lambda(fi) and ž(psi) are given by certain F-norms. As applications we characterize bounded superposition operators on some multiplier sequence spaces of Maddox type.

Słowa kluczowe

EN

sequence space; superposition operators; modulus function; local boundedness

PL

przestrzeń ciągu; operatory superpozycyjne; funkcja modułowa

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 4
• Strony: 869--886
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Molder A.

• Institute of Pure Mathematics University of Tartu Liivi 2, 50409 Tartu, Estonia,

Bibliografia

• [1] F. Dedagich, P. P. Zabreiko, On superposition operators in lp spaces, Sibirsk. Mat. Zh. 28 (1987), no.1, 86–98 (Russian); English translation: Siberian Math. J. 28 (1987), no. 1, 63–73.
• [2] K.-G. Grosske-Erdmann, The structure of the sequence spaces of Maddox, Canad. J. Math. 44 (1992), 298–302.
• [3] Mushir A. Khan, Qamaruddin, Some generalized sequence spaces and related matrix transformations, Far East J. Math. Sci. 5 (1997), 243–252.
• [4] E. Kolk, Inclusion theorems for some sequence spaces defined by a sequence of moduli , Tartu Ül. Toimetised 970 (1994), 65–72.
• [5] E. Kolk, F-seminormed sequence spaces defined by a sequence of modulus functions and strong summability, Indian J. Pure Appl. Math. 28 (1997), 1547–1566.
• [6] E. Kolk, Superposition operators on sequence spaces defined by ?-functions, Demonstratio Math. 37 (2004), 159–175.
• [7] E. Kolk, A. Mölder, The continuity of superposition operators on some sequence spaces defined by moduli , Czechoslovak Math. J. (submitted).
• [8] Y. Luh, Die Räume l(p), l1(p), c(p), c0(p), w(p), w0(p) und w1(p), Mitt. Math. Sem. Giessen 180 (1987), 35–57.
• [9] I. J. Maddox, Sequence spaces defined by a modulus, Math. Proc. Camb. Phil. Soc. 100 (1986), 161–166.
• [10] W. Orlicz, Über konjugierte Exponentenfolgen, Studia Math. 3 (1931), 200–211.
• [11] W. H. Ruckle, FK spaces in which the sequence of coordinate vectors is bounded, Canad. J. Math. 25 (1973), 973–978.
• [12] A. Sama-ae, Boundedness and continuity of superposition operator on Er(p) and Fr(p), Songklanakarin J. Sci. Technol. 24 (2002), 451–466.
• [13] V. Soomer, On the sequence space defined by a sequence of moduli and on the ratespace, Acta Comment. Univ. Tartuensis Math. 1 (1996), 71–74.
• [14] S. Suantai, Boundedness of superposition operators on Er and Fr, Comment. Math. Prace Mat. 37 (1997), 249–259.