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.

Last updated: 09/30/2015