Gupta, A., Mamtani, K. (2017). Variants of Weyl's theorem for direct sums of closed linear operators. Advances in Operator Theory, 2(4), 409-418. doi: 10.22034/aot.1701-1087
Anuradha Gupta; Karuna Mamtani. "Variants of Weyl's theorem for direct sums of closed linear operators". Advances in Operator Theory, 2, 4, 2017, 409-418. doi: 10.22034/aot.1701-1087
Gupta, A., Mamtani, K. (2017). 'Variants of Weyl's theorem for direct sums of closed linear operators', Advances in Operator Theory, 2(4), pp. 409-418. doi: 10.22034/aot.1701-1087
Gupta, A., Mamtani, K. Variants of Weyl's theorem for direct sums of closed linear operators. Advances in Operator Theory, 2017; 2(4): 409-418. doi: 10.22034/aot.1701-1087
Variants of Weyl's theorem for direct sums of closed linear operators
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.