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

Suppose that c is an operator on a Hilbert Space H such that the von Neumann algebra N generated by c is finite. Let τ be a faithful normal tracial state on N and set b1 = (c+ c )/2 and b2 = (c− c)/2i. Also write B for the spectral scale of {b1, b2} relative to τ . In previous work by the present authors, some joint with Nik Weaver, B has been shown to contain considerable spectral information ...

results the results of this study showed high reliability and validity of smartphone in regarding ug with icc > 0.95. the highest reliability for both methods was in elbow supination and the lowest was in the elbow flexion (0.84). objectives the study was designed to compare the smartphone inclinometer-based app and ug in evaluation of rom of elbow. materials and methods the maximum rom of elbo...

This paper shows how C-numerical-range related new strucures may arise from practical problems in quantum control—and vice versa, how an understanding of these structures helps to tackle hot topics in quantum information. We start out with an overview on the role of C-numerical ranges in current research problems in quantum theory: the quantum mechanical task of maximising the projection of a p...