Orbits of linear operators and Banach space geometry

Details Orbits of linear operators and Banach space geometry Orbits of linear operators and Banach space geometry

2012-04-10

arxiv.org/abs/1204.2046v1

Mathematics

Functional Analysis

16 pages

Scientific paper

Let $T$ be a bounded linear operator on a (real or complex) Banach space $X$. If $(a_n)$ is a sequence of non-negative numbers tending to 0. Then, the set of $x \in X$ such that $\|T^nx\| \geqslant a_n \|T^n\|$ for infinitely many $n$'s has a complement which is both $\sigma$-porous and Haar-null. We also compute (for some classical Banach space) optimal exponents $q>0$, such that for every non nilpotent operator $T$, there exists $x \in X$ such that $(\|T^nx\|/\|T^n\|) \notin \ell^{q}(\mathbb{N})$, using techniques which involve the modulus of asymptotic uniform smoothness of $X$.

Affiliated with

Also associated with

No associations

Rating

Orbits of linear operators and Banach space geometry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Orbits of linear operators and Banach space geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Orbits of linear operators and Banach space geometry will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-644366