The classical numerical range of a quadratic operator is an elliptical disk. This result is extended to different kinds of generalized numerical ranges. In particular, it is shown that for a given quadratic operator, the rank-k numerical range, the essential numerical range, and the q-numerical range are elliptical disks; the c-numerical range is a sum of elliptical disks, and the Davis-Wieland...

This paper presents a new video restoration scheme based on the joint sparse and lowrank matrix approximation. By grouping similar patches in the spatiotemporal domain, we formulate the video restoration problem as a joint sparse and low-rank matrix approximation problem. The resulted nuclear norm and `1 norm related minimization problem can also be efficiently solved by many recently developed...

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 ...

Associated with every commuting m-tuples of operators on a complex Hilbert space X is its Aluthge transform. In this paper we show that and transform have the same joint essential spectrum. Further, it shown spectrum contained in numerical range

A bstract We examine strong/weak dualities in two dimensional conformal field theories by generalizing the Fateev-Zamolodchikov-Zamolodchikov (FZZ-)duality between Witten’s cigar model described $$ \mathfrak{sl}(2)/\mathfrak{u}(1) sl 2 / u <m...

background:  the glenohumeral joint becomes dislocated more than any other major joint because it maintains a wide range of motion and its stability is inherently weak. the most common complication following acute initial shoulder dislocation is recurrent dislocation or chronic instability. imbalance of strength and range of motion in individuals with anterior dislocation can be a contributing ...