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- W2962775804 abstract "Let $T$ be a self-adjoint operator on a complex Hilbert space $mathcal{H}$. We give a sufficient and necessary condition for $T$ to be the pencil $lambda P+Q$ of a pair $( P, Q)$ of projections at some point $lambdainmathbb{R}backslash{-1, 0}$. Then we represent all pairs $(P, Q)$ of projections such that $T=lambda P+Q$ for a fixed $lambda$, and find that all such pairs are connected if $lambdainmathbb{R}backslash{-1, 0, 1}$. Afterwards, the von Neumann algebra generated by such pairs $(P,Q)$ is characterized. Moreover, we prove that there are at most two real numbers such that $T$ is the pencils at these real numbers for some pairs of projections. Finally, we determine when the real number is unique." @default.
- W2962775804 created "2019-07-30" @default.
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- W2962775804 date "2019-01-01" @default.
- W2962775804 modified "2023-09-26" @default.
- W2962775804 title "Pencils of pairs of projections" @default.
- W2962775804 doi "https://doi.org/10.4064/sm171222-13-7" @default.
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