We will use Garcı́a-Falset and Lloréns Fuster’s paper on the AMC-property to prove that a Banach space X that 1 δ embeds in a subspace Xδ of a Banach space Y with a 1-unconditional basis has the property AMC and thus the weak fixed point property. We will apply this to some results by Cowell and Kalton to prove that every reflexive real Banach space with the property WORTH and its dual have the ...

let $omega_x$ be a bounded, circular and strictly convex domain of a banach space $x$ and $mathcal{h}(omega_x)$ denote the space of all holomorphic functions defined on $omega_x$. the growth space $mathcal{a}^omega(omega_x)$ is the space of all $finmathcal{h}(omega_x)$ for which $$|f(x)|leqslant c omega(r_{omega_x}(x)),quad xin omega_x,$$ for some constant $c>0$, whenever $r_{omega_x}$ is the m...

We first introduce a modified proximal point algorithm for maximal monotone operators in a Banach space. Next, we obtain a strong convergence theorem for resolvents of maximal monotone operators in a Banach space which generalizes the previous result by Kamimura and Takahashi in a Hilbert space. Using this result, we deal with the convex minimization problem and the variational inequality probl...

A projectional skeleton in a Banach space is a σ-directed family of projections onto separable subspaces, covering the entire space. The class of Banach spaces with projectional skeletons is strictly larger than the class of Plichko spaces (i.e. Banach spaces with a countably norming Markushevich basis). We show that every space with a projectional skeleton has a projectional resolution of the ...

We prove a general result on complemented unconditional basic sequences in Banach lattices and apply it to give some new examples of spaces with unique unconditional basis. We show that Tsirelson space and certain Nakano spaces have unique unconditional bases. We also construct an example of a space with a unique unconditional basis with a complemented subspace failing to have a unique uncondit...

Then Xc is the completion of {X, \\ \\c). Alternatively || ||c is the Minkowski functional of the convex hull of the unit ball. Xc has the property that any bounded linear operator L:X —> Z into a Banach space extends with preservation of norm to an operator L\XC —» Z. The Banach envelope of / (0 < p < 1) is, of course, lx. In 1969, Duren, Romberg and Shields [3] identified the dual space of H_...

Let x be a sequence of real numbers and let p be a real number. The functor x yielding a sequence of real numbers is defined as follows: (Def. 1) For every natural number n holds x(n) = |x(n)|. Let p be a real number. Let us assume that p ≥ 1. The functor l yielding a non empty subset of the carrier of the linear space of real sequences is defined as follows: (Def. 2) For every set x holds x ∈ ...

We present two applications Ball’s extension theorem. First we observe that Ball’s extension theorem, together with the recent solution of Ball’s Markov type 2 problem due to Naor, Peres, Schramm and Sheffilield, imply a generalization, and an alternative proof of, the Johnson-Lindenstrauss extension theorem. Secondly, we prove that the distortion required to embed the integer lattice {0, 1, . ...