(1) If Y is a finite Co-dimensional subspace of a Banach space X and Z is its complementation, is for every projection P0 from X onto Z and every 2 > 0 there a projection P from X onto Y satisfying (1) ‖P‖ ≤ 1 + (1 + 2)‖P0‖? (2) If X is a Banach space, x ∈ X, Y is an n-CO-dimensional subspace of X and ({fi, xi}i=1) is the Auerbach system of the complementation Z of Y in X, is there an element y...

A stronger version of the notion of frame in Banach space called Strong Retro Banach frame (SRBF) is defined and studied. It has been proved that if X is a Banach space such that X ∗ has a SRBF, then X has a Bi-Banach frame with some geometric property. Also, it has been proved that if a Banach space X has an approximative Schauder frame, then X ∗ has a SRBF. Finally, the existence of a non-lin...

For a countable family {Tn}n 1 of strictly pseudo-contractions, a strong convergence of viscosity iteration is shown in order to find a common fixed point of {Tn}n 1 in either a p-uniformly convex Banach space which admits a weakly continuous duality mapping or a p-uniformly convex Banach space with uniformly Gâteaux differentiable norm. As applications, at the end of the paper we apply our res...

We generalize the classical coorbit space theory developed by Feichtinger and Gröchenig to quasi-Banach spaces. As a main result we provide atomic decompositions for coorbit spaces defined with respect to quasi-Banach spaces. These atomic decompositions are used to prove fast convergence rates of best n-term approximation schemes. We apply the abstract theory to time-frequency analysis of modul...

in this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the bag and samanta’s operator norm on felbin’s-type fuzzy normed spaces. in particular, the completeness of this space is studied. by some counterexamples, it is shown that the inverse mapping theorem and the banach-steinhaus’s theorem, are not valid for this fuzzy setting. also...

With this norm, K(W) is a Banach space and even a Banach lattice, i.e., a vector lattice with the property that \g\ ^/, fEk(W) for a measurable g implies gGA(JF) and ||g|| á||/||. Condition (3) ensures [l, Theorem 5] that the norm (4) is continuous with respect to monotone limits. One obtains examples of such functions W as follows. Let (S, B, p.) be a measure space with measure p, which we sha...

Let 1 < q < p < ∞ and q ≤ r ≤ p. Let X be a reflexive Banach space satisfying a lower-lq-tree estimate and let T be a bounded linear operator from X which satisfies an upper-lp-tree estimate. Then T factors through a subspace of ( ∑ Fn)lr , where (Fn) is a sequence of finite-dimensional spaces. In particular, T factors through a subspace of a reflexive space with an (lp, lq) FDD. Similarly, let...

Let P be a class of Banach spaces and let T = {Tα}α∈A be a set of metric spaces. We say that T is a set of test-spaces for P if the following two conditions are equivalent: (1) X / ∈ P; (2) The spaces {Tα}α∈A admit uniformly bilipschitz embeddings into X. The first part of the paper is devoted to a simplification of the proof of the following test-space characterization obtained in M. I. Ostrov...

In this paper, we introduce generalized cyclic φ-contraction maps in metric spaces and give some results of best proximity points of such mappings in the setting of a uniformly convex Banach space. Moreover, we obtain convergence and existence results of proximity points of the mappings on reflexive Banach spaces

In this paper, we study the following operator equation: p ∈ Ax + Cx in a Banach space X , where A : D(A) ⊆ X → 2X is an accretive mapping, C : D(C) ⊆ X → X is a nonlinear mapping and p ∈ X . Various existence results of solutions of nonlinear operator equations in Banach spaces are obtained under a countably condensing type condition. © 2004 Elsevier Ltd. All rights reserved.