We introduce the block numerical range Wn(L ) of an operator function L with respect to a decomposition H = H1⊕ . . .⊕Hn of the underlying Hilbert space. Our main results include the spectral inclusion property and estimates of the norm of the resolvent for analytic L . They generalise, and improve, the corresponding results for the numerical range (which is the case n = 1) since the block nume...

in this paper, we introduce the notions of c-numerical range and c-spectrum of matrix polynomials. some algebraic and geometrical properties are investigated. we also study the relationship between the c-numerical range of a matrix polynomial and the joint c-numerical range of its coefficients.

in this note, a generalization of higher rank numerical range isintroduced and some of its properties are investigated

in this note we characterize polynomial numerical hulls of matrices $a in m_n$ such that$a^2$ is hermitian. also, we consider normal matrices $a in m_n$ whose $k^{th}$ power are semidefinite. for such matriceswe show that $v^k(a)=sigma(a)$.

In this note, a generalization of higher rank numerical range isintroduced and some of its properties are investigated

We prove the operator norm inequality, for a positive matrix partitioned into four blocks in [Formula: see text], text] where is diameter of largest possible disc numerical range text]. This shows that inradius satisfies Several eigenvalue inequalities are derived. In particular, if normal whose spectrum lies radius third full bounded by second sum diagonal block, think optimal and we propose c...