21 citations · 42 across the 40 of their papers we have counts for
5 papers · 2 filters
The normalized numerical range and the Davis-Wielandt shell
Brian Lins, Ilya M. Spitkovsky, Siyu Zhong
For a given -by- matrix , its {\em normalized numerical range} is defined as the range of the function $f_{N,A}\colon x\mapsto (x^*Ax)/(\norm{Ax}\cdot\norm{x})$ o…
Robert Sheckley\s Answerer for two orthogonal projections
Albrecht Boettcher, Ilya Spitkovsky
This paper is the written version of our talk (presented by the second author) at the IWOTA in Chemnitz in August 2017. The meta theorem of the paper is that Halmos' two projection…
A note on Anderson's theorem in the infinite-dimensional setting
Riddhick Birbonshi, Ilya M. Spitkovsky, P. D. Srivastava
Anderson's theorem states that if the numerical range W(A) of an n-by-n matrix A is contained in the unit disk and intersects with the unit circle at more than n points, then it co…
Similarity between two projections
Albrecht Boettcher, Barry Simon, Ilya Spitkovsky
Given two orthogonal projections P and Q, we are interested in all unitary operators U such that UP=QU and UQ=PU. Such unitaries U have previously been constructed by Wang, Du, and…
A distance formula related to a family of projections orthogonal to their symmetries
Ilya M. Spitkovsky
Let u be a hermitian involution, and e an orthogonal projection, acting on the same Hilbert space. We establish the exact formula, in terms of the norm of eue, for the distance fro…