On Algebras Generated by a Partial Isometry

2019 ◽  
Vol 13 (8) ◽  
pp. 3825-3835
Author(s):  
Luoyi Shi ◽  
Sen Zhu
Keyword(s):  
Partial Isometry

scholarly journals Some characterizations of partial isometry elements in rings with involutions

Filomat ◽  
2019 ◽  
Vol 33 (19) ◽  
pp. 6395-6399
Author(s):  
Yinchun Qu ◽  
Hua Yao ◽  
Junchao Wei
Keyword(s):  
Partial Isometry ◽  
Necessary Conditions ◽  
Sufficient And Necessary Conditions

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.

Central Sequence Algebras of a Purely Infinite Simple C*-algebra

2004 ◽  
Vol 56 (6) ◽  
pp. 1237-1258 ◽  
Author(s):  
Akitaka Kishimoto
Keyword(s):  
Fixed Point ◽  
Partial Isometry ◽  
Characterization Result ◽  
C Algebra ◽  
Central Sequence ◽  
Sequence Algebra ◽  
K Theory

AbstractWe are concerned with a unital separable nuclear purely infinite simple C*-algebra A satisfying UCT with a Rohlin flow, as a continuation of [12]. Our first result (which is independent of the Rohlin flow) is to characterize when two central projections in A are equivalent by a central partial isometry. Our second result shows that the K-theory of the central sequence algebra A′ ∩ Aω (for an ω ∈ βN\N) and its fixed point algebra under the flow are the same (incorporating the previous result). We will also complete and supplement the characterization result of the Rohlin property for flows stated in [12].

scholarly journals PARTIAL ISOMETRIES OF A SUB-RIEMANNIAN MANIFOLD

2012 ◽  
Vol 23 (02) ◽  
pp. 1250043
Author(s):  
MAHUYA DATTA
Keyword(s):  
Riemannian Manifold ◽  
Tangent Bundle ◽  
Smooth Manifold ◽  
Partial Isometry ◽  
Riemannian Metric ◽  
Riemannian Structure ◽  
Partial Isometries ◽  
Smooth Map

In this article, we obtain the following generalization of isometric C1-immersion theorem of Nash and Kuiper. Let M be a smooth manifold of dimension m and H a rank k subbundle of the tangent bundle TM with a Riemannian metric gH. Then the pair (H, gH) defines a sub-Riemannian structure on M. We call a C1-map f : (M, H, gH) → (N, h) into a Riemannian manifold (N, h) a partial isometry if the derivative map df restricted to H is isometric, that is if f*h|H = gH. We prove that if f0 : M → N is a smooth map such that df0|H is a bundle monomorphism and [Formula: see text], then f0 can be homotoped to a C1-map f : M → N which is a partial isometry, provided dim N > k. As a consequence of this result, we obtain that every sub-Riemannian manifold (M, H, gH) admits a partial isometry in ℝn, provided n ≥ m + k.

scholarly journals Extensions of symmetric operators I: The inner characteristic function case

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
R.T.W. Martin
Keyword(s):  
Hilbert Space ◽  
Characteristic Function ◽  
Linear Transformation ◽  
Partial Isometry ◽  
Theoretic Characterization ◽  
Symmetric Operators

AbstractGiven 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

scholarly journals Trace Formula for Partial Isometry Case

2009 ◽  
Vol 32 (1) ◽  
pp. 27-32 ◽  
Author(s):  
Muneo CHŌ ◽  
Tadasi HURUYA
Keyword(s):  
Trace Formula ◽  
Partial Isometry

scholarly journals Partial isometry and strongly EP elements

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 2121-2128
Author(s):  
Jiayi Cai ◽  
Zhichao Chen ◽  
Junchao Wei
Keyword(s):  
Partial Isometry ◽  
Necessary Conditions ◽  
Ring Theory ◽  
Important Research ◽  
Sufficient And Necessary Conditions ◽  
Research Objects

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.

scholarly journals On partial isometries with circular numerical range

2021 ◽  
Vol 8 (1) ◽  
pp. 176-186
Author(s):  
Elias Wegert ◽  
Ilya Spitkovsky
Keyword(s):  
Blaschke Product ◽  
Partial Isometry ◽  
Shift Operator ◽  
Numerical Range ◽  
Elliptic Functions ◽  
Blaschke Products ◽  
Partial Isometries ◽  
Unitary Similarity ◽  
Boundary Interpolation ◽  
Poncelet Polygons

Abstract 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.

Strong Extensions vs. Weak Extensions of C*-Algebras

1978 ◽  
Vol 21 (2) ◽  
pp. 143-147
Author(s):  
S. J. Cho
Keyword(s):  
Hilbert Space ◽  
Partial Isometry ◽  
Compact Operators ◽  
Bounded Operators ◽  
Infinite Dimensional ◽  
C Algebras ◽  
Infinite Dimensional Hilbert Space ◽  
Dimensional Hilbert Space ◽  
Image Position ◽  
The Ideal

Let be a separable complex infinite dimensional Hilbert space, the algebra of bounded operators in the ideal of compact operators, and the quotient map. Throughout this paper A denotes a separable nuclear C*-algebra with unit. An extension of A is a unital *-monomorphism of A into . Two extensions τ1 and τ2 are strongly (weakly) equivalent if there exists a unitary (Fredholm partial isometry) U in such thatfor all a in A.

Sign in / Sign up

Export Citation Format

Share Document