Mathematics – Functional Analysis
Scientific paper
2009-05-31
Mathematics
Functional Analysis
Scientific paper
We show that if an infinite-dimensional Banach space X has a symmetric basis then there exists a bounded, linear operator R : X --> X such that the set A = {x in X : ||R^n(x)|| --> infinity} is non-empty and nowhere dense in X. Moreover, if x in X\A then some subsequence of (R^n(x)) converges weakly to x. This answers in the negative a recent conjecture of Prajitura. The result can be extended to any Banach space containing an infinite-dimensional, complemented subspace with a symmetric basis; in particular, all 'classical' Banach spaces admit such an operator.
Hajek Petr
Smith Jeffrey R.
No associations
LandOfFree
Operator machines on directed graphs 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 Operator machines on directed graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Operator machines on directed graphs will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-708672