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Autumn 2017 Variants of Weyl's theorem for direct sums of closed linear operators
Anuradha Gupta, Karuna Mamtani
Adv. Oper. Theory 2(4): 409-418 (Autumn 2017). DOI: 10.22034/aot.1701-1087

Abstract

If $T$ is an operator with compact resolvent and $S$ is any densely defined closed linear operator, then the orthogonal direct sum of $T$ and $S$ satisfies various Weyl type theorems if some necessary conditions are imposed on the operator $S$. It is shown that if $S$ is isoloid and satisfies Weyl's theorem, then $T \oplus S$ satisfies Weyl's theorem. Analogous result is proved for a-Weyl's theorem. Further, it is shown that Browder's theorem is directly transmitted from $S$ to $T \oplus S$. The converse of these results have also been studied.

Citation

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Anuradha Gupta. Karuna Mamtani. "Variants of Weyl's theorem for direct sums of closed linear operators." Adv. Oper. Theory 2 (4) 409 - 418, Autumn 2017. https://doi.org/10.22034/aot.1701-1087

Information

Received: 3 January 2017; Accepted: 7 June 2017; Published: Autumn 2017
First available in Project Euclid: 4 December 2017

zbMATH: 06804217
MathSciNet: MR3730036
Digital Object Identifier: 10.22034/aot.1701-1087

Subjects:
Primary: 47A53
Secondary: 47A10, 47A11

Rights: Copyright © 2017 Tusi Mathematical Research Group

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Vol.2 • No. 4 • Autumn 2017
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