Semi-Fredholm Maps of FK Spaces.
Several order relations in the set of strict t-norms are investigated.
A simple theorem is proved which states a sufficient condition for the sum ot two closed subspaces of a Banach space to be closed. This leads to several analogues of Sarason’s theorem which states that is a closed subalgebra of . In these analogues, the unit circle is replaces by other groups, and the unit disc is replaced by polydiscs or by balls in spaces of several complex variables. Sums of closed ideals in Banach algebras are also studied.
We study the problem of the existence of a common algebraic complement for a pair of closed subspaces of a Banach space. We prove the following two characterizations: (1) The pairs of subspaces of a Banach space with a common complement coincide with those pairs which are isomorphic to a pair of graphs of bounded linear operators between two other Banach spaces. (2) The pairs of subspaces of a Banach space X with a common complement coincide with those pairs for which there exists an involution...