We consider the Banach-Mackey property for pairs of vector spaces E and E′ which are in duality. Let A be an algebra of sets and assume that P is an additive map from A into the projection operators on E. We define a continuous gliding hump property for the map P and show that pairs with this gliding hump property and another measure theoretic property are Banach-Mackey pairs,i.e., weakly bound...

We consider stochastic optimal control problems in Banach spaces, related to nonlinear controlled equations with dissipative non linearity. These problems are treated via the backward stochastic differential equations approach, that allows also to solve in mild sense Hamilton Jacobi Bellman equations in Banach spaces. We apply the results to controlled stochastic heat and wave equations with co...

We consider real spaces only. Definition. An operator T : X → Y between Banach spaces X and Y is called a Hahn-Banach operator if for every isometric embedding of the space X into a Banach space Z there exists a norm-preserving extension T̃ of T to Z. A geometric property of Hahn-Banach operators of finite rank acting between finite-dimensional normed spaces is found. This property is used to ch...

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 ...

Motivated by an Arens regularity problem, we introduce the concepts of matrix Banach space and matrix Banach algebra. The notion of matrix normed space in the sense of Ruan is a special case of our matrix normed system. A matrix Banach algebra is a matrix Banach space with a completely contractive multiplication. We study the structure of matrix Banach spaces and matrix Banach algebras. Then we...

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.

in this paper, we introduce the cone normed spaces and cone bounded linear mappings. among other things, we prove the baire category theorem and the banach--steinhaus theorem in cone normed spaces.

It is a well-known result of Kadec that every two separable infinite dimensional Banach spaces are homeomorphic. Also in large classes of nonseparable Banach spaces (perhaps all) the density character of a Banach space is its only topological invariant (see the book [2] for details). The situation changes considerably if we consider uniform homeomorphisms. Several results are known which prove ...

In this paper, we present a new iterative scheme for finding a common element of the solution set F of the split feasibility problem and the fixed point set F(T) of a right Bregman strongly quasi-nonexpansive mapping T in p-uniformly convex Banach spaces which are also uniformly smooth. We prove strong convergence theorem of the sequences generated by our scheme under some appropriate condition...

There is a subtle difference as far as the invariant subspace problem is concerned for operators acting on real Banach spaces and operators acting on complex Banach spaces. For instance, the classical hyperinvariant subspace theorem of V. I. Lomonosov [10] while true for complex Banach spaces is false for real Banach spaces. When one starts with a bounded operator on a real Banach space and the...