COSAM » Events » 2015 » October » Linear Algebra Seminar

Linear Algebra Seminar |

Time: Oct 06, 2015 (04:00 PM) |

Location: Parker Hall 224 |

Details: Speaker: Deyu Wu Title: The Spectral Equality for Upper Triangular Operator Matrices with Unbounded Entries Let $$M_{C}=\begin{bmatrix}A & C\\ 0 & B\\ \end{bmatrix}: \mathbb{D}(M_{C})\subset X\times X\rightarrow X\times X $$ be a \(2\times 2\) unbounded upper triangular operator matrix in the complex Hilbert space \(X\times X\). We investigate the conditions under which \(\sigma(M_{C})=\sigma(A)\cup\sigma(B)\) holds in the diagonally dominant (\(\mathbb{D}(M_{C})=\mathbb{D}(A)\times\mathbb{D}(B)\)) and upper dominant case (\(\mathbb{D}(M_{C})=\mathbb{D}(A)\times\mathbb{D}(C)\)). Some necessary and sufficient conditions are obtained. |