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.

It is shown that the result of Tso-Wu on the elliptical shape of the numerical range of quadratic operators holds also for the C*-algebra numerical range.

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.

the rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. for noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. in this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, generaliz...

For an $$n\times n$$ complex matrix C, the C-numerical range of a bounded linear operator T acting on Hilbert space dimension at least n is set numbers $$\textrm{tr}\,(CX\,^*\,TX)$$ , where X partial isometry satisfying $$X^*X = I_n$$ . It shown that $$\begin{aligned} \textbf{cl}(W_C(T)) \cap \{\textbf{cl}(W_C(U)): U \hbox { unitary dilation } T\} \end{aligned}$$ for any contraction if and only...