Block numerical range and estimable total decompositions of normal operators
Jiahui Yu, Alatancang Chen · Linear and Multilinear Algebra · 2018
This paper deals with a conjecture posed by Abbas Salemi in 2011 (Banach J. Math. Anal.), claiming that for the spectrum of every bounded linear operator on a separable Hilbert space there exists an estimable total decomposition. We partially solve this problem, in the sense that, for the normal operator, there exists an estimable decomposition, under approximately unitary equivalence.