Total decomposition and block numerical range

Abbas Salemi

doi:10.15352/bjma/1313362979

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Home > Journals > Banach J. Math. Anal. > Volume 5 > Issue 1 > Article

2011 Total decomposition and block numerical range

Abbas Salemi

Banach J. Math. Anal. 5(1): 51-55 (2011). DOI: 10.15352/bjma/1313362979

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Abstract

Let $\mathcal{H}$ be a separable Hilbert space and let $\mathcal{A} \in \mathcal{B}(\mathcal{H})$. In this note the notion of a total decomposition is introduced, and it is shown that sometimes the block numerical ranges corresponding to a total decomposition approximate $\sigma(A),$ sometimes not.