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Orthogonally complemented hyperplanes in Orlicz function spaces

Chen S., Hudzik H., Wang Y.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2004

Vol. 44, nr spec.

71-82

In this paper, necessary and sufficient conditions for a closed hyperplane in Orlicz space to be generalized orthogonally complemented are given for both the Orlicz and the Luxemburg norm. The concept of strongly generalized orthogonally complemented subspace in Banach space is defined and criteria for such subspaces in Orlicz space for both norms are given.

On a generalized orthogonal additivity

Szostok T.

Bulletin of the Polish Academy of Sciences. Mathematics

2001

Vol. 49, no 4

395-408

Some relations between the modified version of the orthogonal Cauchy equation and the following more general equation f(x + y) = g ([...]) [f(x) + f(y)] are obtained. Further the Cauchy equation with the right-hand side multiplied by some constant is considered. This equation is assumed for all x,y satisfying the equality [...] = [alpha]. Finally solutions of this cooditional equation in the case of odd functions defined on inner product spaces and [alpha] lying in some interval are determined.