On quasi-complemented subspaces of Banach spaces, with an Appendix on compactness of operators from Lp(μ) to Lr(ν)

On quasi-complemented subspaces of banach spaces.

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...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

On Contractively Complemented Subspaces

Abstract. It is shown that for an L1-predual space X and a countable linearly independent subset of ext(BX∗) whose norm-closed linear span Y in X∗ is w∗-closed, there exists a w∗-continuous contractive projection from X∗ onto Y . This result combined with those of Pelczynski and Bourgain yields a simple proof of the Lazar-Lindenstrauss theorem that every separable L1-predual with non-separable ...

Compact operators on Banach spaces

In this note I prove several things about compact linear operators from one Banach space to another, especially from a Banach space to itself. Some of these may things be simpler to prove for compact operators on a Hilbert space, but since often in analysis we deal with compact operators from one Banach space to another, such as from a Sobolev space to an L space, and since the proofs here are ...