Partial isometries
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Partial Isometries and EP Elements in Banach Algebras
and Applied Analysis 3 The left multiplication by a ∈ A is the mapping La : A → A, which is defined as La x ax for all x ∈ A. Observe that, for a, b ∈ A, Lab LaLb and that La Lb implies a b. If a ∈ A is both Moore-Penrose and group invertible, then La† La † and La# La # in the Ba
On Certain Automorphisms of Sets of Partial Isometries
Under the mild condition of continuity at a single point we describe all the bijections of the set of all partial isometries on a Hilbert space which preserve the order and the orthogonality in both directions. Moreover, we present a natural analogue of Wigner’s theorem on quantu
On the Universal C∗-algebra Generated by Partial Isometry
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
Globalization of the partial isometries of metric spaces and local approximation of the group of isometries of Urysohn space
We prove the equivalence of the two important facts about finite metric spaces and universal Urysohn metric spaces U, namely theorem A and theorem B below: Theorem A (Approximation): The group of isometry ISO(U) contains everywhere dense locally finite subgroup; Theorem G(Globali
D ec 1 99 7 PARTIAL DYNAMICAL SYSTEMS AND C ∗ - ALGEBRAS GENERATED BY PARTIAL ISOMETRIES
A collection of partial isometries whose range and initial projections satisfy a specified set of conditions often gives rise to a partial representation of a group. The Calgebra generated by the partial isometries is thus a quotient of the universal C-algebra for partial represe
Partial Orders on Partial Isometries
This paper studies three natural pre-orders of increasing generality on the set of all completely non-unitary partial isometries with equal defect indices. We show that the problem of determining when one partial isometry is less than another with respect to these pre-orders is e