Abstract. We consider three lifting questions: Given a C∗-algebra I, if there is a unital C∗-algebra A contains I as an ideal, is every unitary from A/I lifted to a unitary in A? is every unitary from A/I lifted to an extremal partial isometry? is every extremal partial isometry from A/I lifted to an extremal partial isometry? We show several constructions of I which serve as working examples o...

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

We show that a finite metric space A admits an extension to a finite metric space B so that each partial isometry of A extends to an isometry of B. We also prove a more precise result on extending a single partial isometry of a finite metric space. Both these results have consequences for the structure of the isometry groups of the rational Urysohn metric space and the Urysohn metric space.

In this paper we characterize weighted substitution operators between L-spaces of vector-valued functions and also make an attempt to characterize isometry and partial isometry of these operators.

We determine when a matrix is similar to a partial isometry, refining a result of Halmos–McLaughlin.

A universal C∗-algebra is constructed which is generated by a partial isometry. Using grading on this algebra we construct an analog of Cuntz algebras which gives a homotopical interpretation of KK-groups. It is proved that this algebra is homotopy equivalent up to stabilization by 2×2 matrices to M2(C). Therefore those algebras are KK-isomorphic. We recall the definition of partial isometry. D...