Weak group inverses and partial isometries in proper *-rings

In proper ∗-rings, we characterize weak group inverses by three equations. It generalizes the notion of weak group inverse, which was introduced by Wang and Chen for complex matrices in 2018. Some new equivalent characterizations for elements to be weak group invertible are presented. Furthermore, we define the group-EP decomposition. Some properties of the weak group inverse are established by the group-EP decomposition.

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m-weak group inverses in a ring with involution

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas ◽

10.1007/s13398-020-00932-1 ◽

2020 ◽

Vol 115 (1) ◽

Author(s):

Yukun Zhou ◽

Jianlong Chen ◽

Mengmeng Zhou

Keyword(s):

Weak Group ◽

Group Inverses

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Metric geometry of partial isometries in a finite von Neumann algebra

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2007.04.056 ◽

2008 ◽

Vol 337 (2) ◽

pp. 1226-1237 ◽

Cited By ~ 1

Author(s):

Esteban Andruchow

Keyword(s):

Von Neumann Algebra ◽

Metric Geometry ◽

Partial Isometries ◽

Von Neumann ◽

Finite Von Neumann Algebra

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CUNTZ–PIMSNER C*-ALGEBRAS ASSOCIATED WITH SUBSHIFTS

International Journal of Mathematics ◽

10.1142/s0129167x0800456x ◽

2008 ◽

Vol 19 (01) ◽

pp. 47-70 ◽

Cited By ~ 15

Author(s):

TOKE MEIER CARLSEN

Keyword(s):

Partial Isometries ◽

C Algebra ◽

C Algebras ◽

Shift Space

By using C*-correspondences and Cuntz–Pimsner algebras, we associate to every subshift (also called a shift space) 𝖷 a C*-algebra [Formula: see text], which is a generalization of the Cuntz–Krieger algebras. We show that [Formula: see text] is the universal C*-algebra generated by partial isometries satisfying relations given by 𝖷. We also show that [Formula: see text] is a one-sided conjugacy invariant of 𝖷.

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