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- W4301658966 abstract "Let $mathbf{T}$ be a pair of commuting hyponormal operators satisfying the so-called quasitriangular property $$ textrm{dim} ; textrm{ker} ; (mathbf{T}-boldsymbollambda) ge textrm{dim} ; textrm{ker} ; (mathbf{T} - {boldsymbollambda})^*), $$ for every $boldsymbollambda$ in the Taylor spectrum $sigma(mathbf{T})$ of $mathbf{T}$. We prove that the Weyl spectrum of $mathbf{T}$, $omega(mathbf{T})$, satisfies the identity $$ omega(mathbf{T})=sigma(mathbf{T}) setminus pi_{00}(mathbf{T}), $$ where $pi_{00}(mathbf{T})$ denotes the set of isolated eigenvalues of finite multiplicity. Our method of proof relies on a (strictly $2$-variable) fact about the topological boundary of the Taylor spectrum; as a result, our proof does not hold for $d$-tuples of commuting hyponormal operators with $d>2$." @default.
- W4301658966 created "2022-10-05" @default.
- W4301658966 creator A5066109793 @default.
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- W4301658966 date "2017-10-29" @default.
- W4301658966 modified "2023-10-01" @default.
- W4301658966 title "Weyl's Theorem for pairs of commuting hyponormal operators" @default.
- W4301658966 doi "https://doi.org/10.48550/arxiv.1710.10680" @default.
- W4301658966 hasPublicationYear "2017" @default.
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