On pairs of Banach spaces which are isomorphic to complemented subspaces of each other

On quasi-complemented subspaces of banach spaces.

ON BANACH SPACES WHOSE DUALS ARE ISOMORPHIC TO l1(Γ)

In this paper we present new characterizations of Banach spaces whose duals are isomorphic to l1(Γ), extending results of Stegall, Lewis-Stegall and Cilia-D’Anna-Gutiérrez.

Closed Ideals of Operators on and Complemented Subspaces of Banach Spaces of Functions with Countable Support

Let λ be an infinite cardinal number and let `∞(λ) denote the subspace of `∞(λ) consisting of all functions which assume at most countably many non zero values. We classify all infinite dimensional complemented subspaces of `∞(λ), proving that they are isomorphic to `∞(κ) for some cardinal number κ. Then we show that the Banach algebra of all bounded linear operators on `∞(λ) or `∞(λ) has the u...

Complemented Subspaces of Spaces Obtained by Interpolation

If Z is a quotient of a subspace of a separable Banach space X, and V is any separable Banach space, then there is a Banach couple (A0, A1) such that A0 and A1 are isometric to X ⊕ V , and any intermediate space obtained using the real or complex interpolation method contains a complemented subspace isomorphic to Z. Thus many properties of Banach spaces, including having non-trivial cotype, hav...

Contractively Complemented Subspaces of Pre-symmetric Spaces

In 1965, Ron Douglas proved that if X is a closed subspace of an L-space and X is isometric to another L-space, then X is the range of a contractive projection on the containing L-space. In 1977 Arazy-Friedman showed that if a subspace X of C1 is isometric to another C1-space (possibly finite dimensional), then there is a contractive projection of C1 onto X. In 1993 Kirchberg proved that if a s...