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arXiv · 1908.03555

The angle along a curve and range-kernel complementarity

Dimosthenis Drivaliaris·Nikos Yannakakis
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Abstract

In this paper, we define the angle of a bounded linear operator $A$ along an unbounded path emanating from the origin and use it to characterize range-kernel complementarity. In particular we show that if $0$ faces the unbounded component of the resolvent set, then $X=R(A)\oplus N(A)$ if and only if $R(A)$ is closed and some angle of $A$ is less than $\pi$.

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Dimosthenis Drivaliaris, Nikos Yannakakis. 2019-08-09. The angle along a curve and range-kernel complementarity. https://arxiv.org/abs/1908.03555

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