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#### Keywords

Operator matrix, Generalized left (right) Weyl, Spectrum

#### Abstract

In this paper, for given operators $A\in\B(\H)$ and $B\in\B(\K)$, the sets of all $C\in \B(\K,\H)$ such that $M_C=\bmatrix{cc} A&C\\0&B\endbmatrix$ is generalized Weyl and generalized left (right) Weyl, are completely described. Furthermore, the following intersections and unions of the generalized left Weyl spectra $$ \bigcup_{C\in\B(\K,\H)}\sigma^g_{lw}(M_C) \;\;\; \mbox{and} \;\;\; \bigcap_{C\in\B(\K,\H)}\sigma^g_{lw}(M_C) $$ are also described, and necessary and sufficient conditions which two operators $A\in\B(\H)$ and $B\in\B(\K)$ have to satisfy in order for $M_C$ to be a generalized left Weyl operator for each $C\in\B(\K,\H)$, are presented.

#### Recommended Citation

Hai, Guojun and Cvetkovic-Ilic, Dragana S..
(2017),
"Generalized left and right Weyl spectra of upper triangular operator matrices",
*Electronic Journal of Linear Algebra*,
Volume 32, pp. 41-50.

DOI: http://dx.doi.org/10.13001/1081-3810.3373

*Abstract*