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Köthe–Toeplitz duals of some vector-valued Orlicz sequence spaces. (English) Zbl 1096.46008
Summary: We obtain the generalized Köthe–Toeplitz duals of some vector-valued Orlicz sequence spaces. We extend the definition of 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 [D. Ghosh and 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 \(F(X_k,M)\).
MSC:
46A45 Sequence spaces (including Köthe sequence spaces)
46A20 Duality theory for topological vector spaces
46B45 Banach sequence spaces
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