The sums of closed subspaces in a topological linear space

Journal of Inequalities and Applications, 2009

2019

In this paper, we prove a Reich-type fixed point theorem in modular spaces. Also, we introduce the concept of h-convex modular spaces and we get the related Banach-type theorem. Our results generalize several ones in the existing literature. Moreover, some examples are given supporting theoretical approaches.

Journal of the London Mathematical Society, 1974

1991

Arkiv för matematik, 1978

Applied Mathematics, 2013

In this paper, we present and discuss the topology of modular spaces using the filter base and we then characterize closed subsets as well as its regularity.

Glasgow Mathematical Journal, 1985

Annali di Matematica Pura ed Applicata, 1988

It is proved that there exist complemented subspaces of countable topological products (locally convex direct sums) of Banach spaces which cannot be represented as topological products (locally convex direct sums) of Banach spaces 1991 Mathematics Subject Classification. Primary 46A04, 46A13, Secondary 47B99.

We show that reexivity of a Banach space can be characterized by a simple prop- erty formulated in terms of the distance to the intersection of a decreasing countable family of closed subspaces. We provide some explicit examples of the failure of the property in the non-reexive case.

arXiv (Cornell University), 2020

For i = 1, 2, let E i be a reflexive Banach lattice over R with a certain parameter λ + (E i) > 1, let K i be a locally compact (Hausdorff) topological space and let H i be a closed subspace of C 0 (K i , E i) such that each point of the Choquet boundary Ch H i K i of H i is a weak peak point. We show that if there exists an isomorphism T : H 1 → H 2 with T • T −1 < min{λ + (E 1), λ + (E 2)} such that T and T −1 preserve positivity, then Ch H 1 K 1 is homeomorphic to Ch H 2 K 2. 2010 Mathematics Subject Classification. 47B38; 46A55.