This is an announcement for the paper "The angle of an operator and range and kernel complementarity" by Dimosthenis Drivaliaris and Nikos Yannakakis.

Abstract: We show that if the angle of a bounded linear operator on a Banach space with closed range is less than $\pi$, then its range and kernel are complementary. We also show that in finite dimensions and up to rotations this simple geometric property characterizes operators for which range and kernel are complementary. For operators on a Hilbert space we present a sufficient condition, involving the distance of the boundary of the numerical range from the origin, for the range and the kernel to be complementary.

Archive classification: math.FA

Mathematics Subject Classification: 47A05, 47A12, 47A10, 47B44, 46B20

Submitted from: d.drivaliaris@fme.aegean.gr

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1409.4195

or

http://arXiv.org/abs/1409.4195