Let E and F be Banach spaces. We say that E is F -saturated if every infinite dimensional closed subspace of E contains an isomorphic copy of F . In [2], it is shown that there exists a c0-saturated Banach space with an unconditional basis whose dual contains an isomorphic copy of l2. In this note, we give an example where the dual situation occurs. It is shown that there is a Banach space with...

We characterize those classes C of separable Banach spaces for which there exists a separable Banach space Y not containing l1 and such that every space in the class C is a quotient of Y .

We give some fixed point theorems for firmly pseudo-contractive mappings defined on nonconvex subsets of a Banach space. We also prove some fixed point results for firmly pseudo-contractive mappings with unbounded nonconvex domain in a reflexive Banach space.

The paper is devoted to two particular cases of the following general problem. Let α and β be two types of bases in Banach spaces. Let a Banach space X has bases of both types and a subspace M ⊂ X∗ contains the sequence of biorthogonal functionals of some α-basis in X. Does M contain a sequence of biorthogonal functionals of some β-basis in X? The following particular cases are considered: (α, ...

Given any Banach space X, let L X 2 denote the Banach space of all measurable functions f : [0, 1] → X for which f 2 := 1 0 f (t) 2 dt

When X is a compact Hausdorff space and E is a real Banach space there is a considerable literature on extremal properties of the space C(X,E) of continuous E-valued functions on X. What happens if the Banach spaces in which the functions on X take their values vary over X? In this paper, we obtain some extremal results on the section space Γ(π) and its dual Γ(π)∗ of a real Banach bundle π : → ...

ð2Þ ~ T 1⁄4 T ; 8 2 V: We use HBðV;W Þ to denote the set of Hahn–Banach operators. The classical Hahn–Banach theorem states that every rank-1 operator from V into W is a Hahn–Banach operator. It can also be restated in the following way: if dimW 1⁄4 1, then HBðV;W Þ 1⁄4 LðV;W Þ. Observe that the two statements above are slightly different. In the first case we describe a property of an operator...

We use several fundamental results which characterize frames for a Hilbert space to give natural generalizations of Hilbert space frames to general Banach spaces. However, we will see that all of these natural generalizations (as well as the currently used generalizations) are equivalent to properties already extensively developed in Banach space theory. We show that the dilation characterizati...

in this paper we give conditions for a tuple of commutative bounded linear operators which holds in the property of the hypercyclicity criterion. we characterize topological transitivity and semi-hereiditarily of a dynamical system given  by an n-tuple of operators acting on a separable infinite dimensional banach space .