Related papers: A note on a diffeomorphism between two Banach spac…

In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.

The paper is devoted to obtaining conditions for the roughness of dichotomy in the Banach spaces. Deep analysis of the well known papers was considered. The main results also works for the case of unbounded operators.

We prove several abstract results giving general conditions under which subspaces of linear or multilinear operators on Banach spaces or Banach lattices are closed. Each of these abstract results is followed by concrete applications,…

The problems connected with equivalent norms lie at the heart of Banach space theory. This is a short survey on some recent as well as classical results and open problems in renormings of Banach spaces.

I investigate a class of dynamical systems in which finite pieces of spacetime contain finite amounts of information. Most of the guiding principles for designing these systems are drawn from general relativity: the systems are…

Let $M$ be a closed manifold and let $N$ be a connected manifold without boundary. For each $k\in\mathbb{N}$ the set of $k$ times continuously differentiable maps between $M$ and $N$ has the structure of a smooth Banach manifold where the…

The classical approach to the study of dynamical systems consists in representing the dynamics of the system in the form of a "source-sink", that means identifying an attractor-repeller pair, which are attractor-repellent sets for all other…

It is known that a Banach space contains an isomorphic copy of $c_0$ if, and only if, it can be equivalently renormed to be almost square. We introduce and study transfinite versions of almost square Banach spaces with the purpose to relate…

We show that the classes of separable reflexive Banach spaces and of spaces with separable dual are strongly bounded. This gives a new proof of a recent result of E. Odell and Th. Schlumprecht, asserting that there exists a separable…

We present some extensions of classical results that involve elements of the dual of Banach spaces, such as Bishop-Phelp's theorem and James' compactness theorem, but restricting to sets of functionals determined by geometrical properties.…

For a compact $(2n+1)$-dimensional smooth manifold, let $\mu_M : B Diff_\partial (D^{2n+1}) \to B Diff (M)$ be the map that is defined by extending diffeomorphisms on an embedded disc by the identity. By a classical result of Farrell and…

We prove a stability theorem for spaces of smooth concordance embeddings. From it we derive various applications to spaces of concordance diffeomorphisms and homeomorphisms.

We prove that a necessary condition for the existence of the remaining problem in the harmonic Hopf construction is also sufficient. We also give some topological applications based on our result.

An L-embedded Banach spaace is a Banach space which is complemented in its bidual such that the norm is additive between the two complementary parts. On such spaces we define a topology, called an abstract measure topology, which by known…

We consider weighted banach spaces of holomorphic functions on the upper half plane that are determined by $ \|f\|=\sup_{y>0,-\infty<x<\infty}p(y)|f(x+iy)|<\infty $ for a very large class of weight functions p. We completely solve the…

The duality of uniform approximation property for Banach spaces is well known. In this note, we establish, under the assumption of local reflexivity, the duality of uniform approximation property in the category of operator spaces.

We prove several unique continuation results for biharmonic maps between Riemannian manifolds.

In this work, we construct and study certain classes of infinite dimensional Lie groups that are modelled on weighted function spaces. In particular, we construct a Lie group of weighted diffeomorphisms on a Banach space. Further, we also…

In this paper, two generalized algorithms for solving the variational inequality problem in Banach spaces are proposed. Then the strong convergence of the sequences generated by these algorithms will be proved under the suitable conditions.…

In this paper Hilbert spaces are characterized among Banach spaces in terms of transitivity with respect to nicely behaved subgroups of the isometry group. For example, the following result is typical here: If X is a real Banach space…