On partial isometries with circular numerical range

In their LAMA 2016 paper Gau, Wang and Wu conjectured that a partial isometry A acting on ℂ n cannot have a circular numerical range with a non-zero center, and proved this conjecture for n ≤ 4. We prove it for operators with rank A = n − 1 and any n. The proof is based on the unitary similarity of A to a compressed shift operator SB generated by a finite Blaschke product B. We then use the description of the numerical range of SB as intersection of Poncelet polygons, a special representation of Blaschke products related to boundary interpolation, and an explicit formula for the barycenter of the vertices of Poncelet polygons involving elliptic functions.

Partial isometry and strongly EP elements

EP elements are important research objects in the ring theory. This paper mainly gives sufficient and necessary conditions for an element in a ring to be an EP element, partial isometry, and strongly EP element by using solutions of certain equations.

Some characterizations of partial isometry elements in rings with involutions

We give some sufficient and necessary conditions for an element in a ring with involution to be a partial isometry by using certain equations admitting solutions in a definite set.

Extensions of symmetric operators I: The inner characteristic function case

Given a symmetric linear transformation on a Hilbert space, a natural problem to consider is the characterization of its set of symmetric extensions. This problem is equivalent to the study of the partial isometric extensions of a fixed partial isometry. We provide a new function theoretic characterization of the set of all self-adjoint extensions of any symmetric linear transformation B with finite equal indices and inner Livšic characteristic function θ

KARAKTERISTIK OPERATOR HIPONORMAL-p PADA RUANG HILBERT

This article discusses the definition and properties of p-hiponormal operators for p>0. To investigate the properties of p-hiponormal operators, the concept of positive operators, partial isometry operators, decomposition of operators, and existence of partial isometry operators for any operator on a Hilbert space are required.