A note on annihilator and complemented Banach aigebras

On quasi-complemented subspaces of banach spaces.

A Note on Αcozero-complemented Spaces and Αborel Sets

α is a regular cardinal number or the symbol ∞, and X is a compact Hausdorff space. It is shown that (Theorem 2.1) X is αcozerocomplemented iff each αBorel set differs from an αcozero set by a meagre set. This immediately yields (Corollary 2.2) X is αdisconnected iff each αBorel set differs from a clopen set by a meagre set. (The cases α = ∞ in Theorem 2.1, and α = ω1 in Corollary 2.2 are impor...

A note on supermodular sublattices in finite relatively complemented lattices

A sublattice in a lattice is called supermodular if, for every two elements, one of which belongs to the sublattice, at least one of their meet and join also belongs to the sublattice. In this note, we describe supermodular sublattices in products of relatively complemented lattices.

A note on essentially left $phi$-contractible Banach algebras

In this note, we show that cite[Corollary 3.2]{sad} is not always true. In fact, we characterize essential left $phi$-contractibility of the group algebras in terms of compactness of its related locally compact group. Also, we show that for any compact commutative group $G$, $L^{2}(G)$ is always essentially left $phi$-contractible. We discuss the essential left $phi$-contractibility of some Fou...

A Note on Fusion Banach Frames

For a fusion Banach frame ({Gn, vn}, S) for a Banach space E, if ({v∗ n(E), v∗ n}, T ) is a fusion Banach frame for E∗, then ({Gn, vn}, S; {v∗ n(E), v∗ n}, T ) is called a fusion bi-Banach frame for E. It is proved that if E has an atomic decomposition, then E also has a fusion bi-Banach frame. Also, a sufficient condition for the existence of a fusion bi-Banach frame is given. Finally, a chara...