On diffeomorphisms deleting weak compacta in Banach spaces

On Diffeomorphisms Deleting Weakly Compacta in Banach Spaces

We prove that if X is an infinite-dimensional Banach space with Cp smooth partitions of the unity then X and X \K are Cp diffeomorphic, for every weakly compact set K ⊂ X.

Weak Interpolation in Banach Spaces

Equivalence of Families of Diffeomorphisms on Banach Spaces

We consider two families of C∞-diffeomorphisms (with hyperbolic linear part at 0) on a Banach space. Suppose that these two families formally conjugate at 0. We prove that they admit local conjugation, which is infinitely smooth in both, the space variable and the family parameter. In particular, subject to non-resonance condition, there exists a family of local C∞ linearizations of the family ...

Weak Thresholding Greedy Algorithms in Banach Spaces

We consider weak thresholding greedy algorithms with respect to Markushevich bases in general Banach spaces. We find sufficient conditions for the equivalence of boundedness and convergence of the approximants. We also show that if there is a weak thresholding algorithm for the system which gives the best n-term approximation up to a multiplicative constant, then the system is already “greedy”....

On Weak Exponential Expansiveness of Evolution Families in Banach Spaces

The aim of this paper is to give several characterizations for the property of weak exponential expansiveness for evolution families in Banach spaces. Variants for weak exponential expansiveness of some well-known results in stability theory (Datko (1973), Rolewicz (1986), Ichikawa (1984), and Megan et al. (2003)) are obtained.