We study new sequence spaces associated to sequences in normed spaces and the band matrix F̂ defined by the Fibonacci sequence. We give some characterizations of continuous linear operators and weakly unconditionally Cauchy series by means of completeness of the new sequence spaces. Also, we characterize the barreledness of a normed space via weakly∗ unconditionally Cauchy series in [Formula: se...

In this note, we will discuss how to relate an operator ideal on Banach spaces to the sequential structures it defines. Concrete examples of ideals of compact, weakly compact, completely continuous, Banach-Saks and weakly Banach-Saks operators will be demonstrated.

We study a class of left-invertible operators which we call weakly concave operators. It includes the and some subclasses expansive strict $m$ -isometries with $m > 2$ . prove Wold-type decomposition for also obtain Berger–Shaw-type theorem analytic finitely cyclic The proofs these results rely heavily on spectral dichotomy provides fairly close relationship, written in terms reciprocal auto...

The purposes of this note are to complement the results of [4] by citing examples of spectral operators (in the sense of that paper) on non-normable locally convex spaces and to announce a result on the structure of spectral operators which indicates that these examples exhibit rather typical behavior for spectral operators on a large class of locally convex spaces of interest to analysts. We r...

Abstract We consider the third order Benjamin-Ono equation on torus ? t u = x ( ? 3 2 H ) + . prove that for any ? R , flow map continuously extends to r 0 s T if ? but does not admit a continuous extension 1 Moreover, we show is weakly sequentially in > L then classify traveling wave solutions and study their orbital stability.

A bounded linear operator between Banach spaces is called completely continuous if it carries weakly convergent sequences into norm convergent sequences. Isolated is a universal operator for the class of non-completely-continuous operators from L1 into an arbitrary Banach space, namely, the operator from L1 into l∞ defined by