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Spaces of type H + C

Walter Rudin (1975)

Annales de l'institut Fourier

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 H + C is a closed subalgebra of L . 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.

Subspaces with a common complement in a Banach space

Dimosthenis Drivaliaris, Nikos Yannakakis (2007)

Studia Mathematica

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...

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