Continuous matrix transformations on sequence spaces with respect to strong $phi$ topology

ISSN: 1300-1833
Yayın Aralığı: Yıllık
Yayıncı: -

S bütün kompleks dizilerin uzayı, X ve Y, S nin iki alt vektör uzayı ve $varphi$ de S deki sonlu dizilerin alt uzayı olsun. Bu makalede a) $varphi$ nin bütün S- sınırlı kümeleri belirlenmiştir, b) Güçlü $varphi$- topolojisine göre X den Y ye sürekli olan bütün matrisler karakterize edilmiştir.

Dizi uzayları üzerinde güçlü $phi$ topolojisine göre sürekli matris dönüşümleri

Let S be the vector space of all complex sequences, X and Y be any two subspaces of S and $varphi$ be the vector space of sequences which have only a finite number of non-zero terms. In this paper a) we describe all S-bounded subsets of $varphi$ ; b) we precisely characterize the matrix transformations from X into Y which are continuous with respect to strong $varphi$-topologies on X and Y.

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1.Heuser, Harro G.: Functional Analysis,(translated by John Horvath, Univ. of Maryland).New York. A Wiley-Interscience Publication 1982.
2.Larsen, R; Functional Analysis. Marcel Dekker, Inc. New York, 1973.
3.Robertson, A.P.; Robertson , Wendy.: Topological vector spaces. Cambridge Univ. Press. Cambridge 1964, 1973.
4.Ruckle, William H.: Topologies on sequence spaces. Pacific J. Math.42 (1972), 235—249.
5.Magee J C; Ruckle, William H.: The strong topology on the dual space of a summability field and the mu-continuity. Math. Z.195(1987),no.3, 409-413.
6.Ruckle, William H.: The Mackey and strong topologies on Köthe sequence spaces. Indiana Univ. Math. J.28(1978), no. 3, 505—513.
7.Ruckle, William H.: The strong p -topologies on symmetric sequence spaces. Canad. J.Math. 37(1985), no,6, 1112-1133.