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Solidity in sequence spaces.

I. J. Maddox (1991)

Revista Matemática de la Universidad Complutense de Madrid

Relations are established between several notions of solidity in vector-valued sequence spaces, and a generalized Köthe-Toeplitz dual space is introduced in the setting of a Banach algebra.

Some approximation results in Musielak-Orlicz spaces

Ahmed Youssfi, Youssef Ahmida (2020)

Czechoslovak Mathematical Journal

We prove the continuity in norm of the translation operator in the Musielak-Orlicz L M spaces. An application to the convergence in norm of approximate identities is given, whereby we prove density results of the smooth functions in L M , in both the modular and norm topologies. These density results are then applied to obtain basic topological properties.

Some classes of infinitely differentiable functions

G. S. Balashova (1999)

Mathematica Bohemica

For nonquasianalytical Carleman classes conditions on the sequences { M ^ n } and { M n } are investigated which guarantee the existence of a function in C J { M ^ n } such that u(n)(a) = bn,    bnKn+1Mn,    n = 0,1,...,    aJ. Conditions of coincidence of the sequences { M ^ n } and { M n } are analysed. Some still unknown classes of such sequences are pointed out and a construction of the required function is suggested. The connection of this classical problem with the problem of the existence of a function with given trace at the boundary...

Some classical function systems in separable Orlicz spaces

C. Finet, G. Tkebuchava (1996)

Studia Mathematica

The boundedness of (sub)sequences of partial Fourier and Fourier-Walsh sums in subspaces of separable Orlicz spaces is studied. The boundedness of the shift operator and Paley function with respect to the Haar system is also investigated. These results are applied to get the analogues of the classical theorems on basicness of the trigonometric and Walsh systems in nonreflexive separable Orlicz spaces.

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