Let λ̂ be an open, Landau subset. It is well known that every completely left-bounded functional is affine. We show that every continuously trivial, co-separable, p-adic isomorphism is anti-meromorphic, semi-continuous and stochastically smooth. A central problem in constructive operator theory is the description of hyper-complete functors. A useful survey of the subject can be found in [5].

In this paper, we study a generalized Sturm-Liouville boundaryvalue problems with two positive parameters. By constructing a completely continuous operator and combining fixed point index theorem and some properties of the eigenvalues of linear operators, we obtain sufficient conditions for the existence of at least one positive solution.

By transforming the boundary value problem into the corresponding fixed-point problem of a completely continuous operator, the existence is obtained in the paper for two-point boundary value problem of fourth order superlinear singular semipositone differential system via the fixed point theorem concerning cone compression and expansion in norm type.

In this note, we will discuss how to relate an operator ideal on Banach spaces to the sequential structures it defines. Concrete examples of ideals of compact, weakly compact, completely continuous, Banach-Saks and weakly Banach-Saks operators will be demonstrated.

Let V,W∞, andW be operator ideals of completely continuous, weakly ∞-compact, and weakly compact operators, respectively. We prove that V =W∞ ◦W−1. As an immediate application, the recent result by Dowling, Freeman, Lennard, Odell, Randrianantoanina, and Turett follows: the weak Grothendieck compactness principle holds only in Schur spaces.