an:05010125
Zbl 1096.46008
Yilmaz, Yilmaz; Özdemir, M. Kemal
Köthe--Toeplitz duals of some vector-valued Orlicz sequence spaces
EN
Soochow J. Math. 31, No. 3, 389-402 (2005).
0250-3255
2005
j
46A45 46A20 46B45
Köthe-Toeplitz dual; vector-valued Orlicz space
Summary: We obtain the generalized Köthe--Toeplitz duals of some vector-valued Orlicz sequence spaces. We extend the definition of \textit{I.~J.\ Maddox} [Int.\ J.\ Math.\ Math.\ Sci.\ 3, 423--432 (1980; Zbl 0464.46014)] a bit, and find the \(\alpha\)-dual of \(F(X_k,M)\) defined in [\textit{D.~Ghosh} and \textit{P.~D.\ Srivastava}, Indian J.\ Pure Appl.\ Math.\ 30, No.~8, 819--826 (1999; Zbl 0935.46008)]. Further, we calculate the \(\beta\)-dual of \(h(X_k,M)\) and \(\ell(X_k,M)\), which are the most important special cases of \(F(X_k,M)\). Several Orlicz sequence spaces such as \(\ell_M\) and \(\ell_M(X)\) are only special cases of \(\ell(X_k,M)\) as well as of \(F(X_k,M)\).
0464.46014; 0935.46008