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...

aim: abnormal joint mobility is an important factor in movement dysfunction and physical disability. a general lack of descriptive details exists for measurements of hip rotation range of motion (rom). this study was designed to establish the influence of hip position on active and passive range of motion of the hip in external and internal rotation(ext & int rot). material & methods: ...

For a noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the joint rank-k numerical range associated with the error operators of the channel is non-empty. In this paper, geometric properties of the joint rank k-numerical range are obtained and their implications to quantum computing are discussed. It is shown that for a given k if the dimension of the un...