Complemented Subspaces in the Normed Spaces

A New Class of Banach Sequence Spaces

Dynamics of non-expansive maps on strictly convex Banach spaces

This paper concerns the dynamics of non-expansive maps on strictly convex finite dimensional normed spaces. By using results of Edelstein and Lyubich, we show that if X = (R, ‖ · ‖) is strictly convex and X has no 1-complemented Euclidean plane, then every bounded orbit of a non-expansive map f : X → X , converges to a periodic orbit. By putting extra assumptions on the derivatives of the norm,...

Weak*-closed invariant subspaces and ideals of semigroup algebras on foundation semigroups

Let S be a locally compact foundation semigroup with identity and                          be its semigroup algebra. Let X be a weak*-closed left translation invariant subspace of    In this paper, we prove that  X  is invariantly  complemented in   if and  only if  the left ideal  of    has a bounded approximate identity. We also prove that a foundation semigroup with identity S is left amenab...

One-complemented subspaces of Musielak-Orlicz sequence spaces

The aim of this paper is to characterize one-complemented subspaces of finite codimension in the Musielak–Orlicz sequence space l . We generalize the well-known fact (Ann. Mat. Pura Appl. 152 (1988) 53; Period. Math. Hungar. 22 (1991) 161; Classical Banach Spaces I, Springer, Berlin, 1977) that a subspace of finite codimension in lp, 1 p<∞, is one-complemented if and only if it can be expressed...

Topological Properties of Real Normed Space

In this article, we formalize topological properties of real normed spaces. In the first few parts, open and closed, density, separability and sequence and its convergence are discussed. Then we argue properties of real normed subspace. In the middle of the article, we discuss linear functions between real normed speces. Several kinds of subspaces induced by linear functions such as kernel, ima...