Advances in Operator Theory

Partial isometries: a survey

Francisco J Fernández-Polo and Antonio Peralta

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Abstract

We survey the main results characterizing partial isometries in C$^*$-algebras and tripotents in JB$^*$-triples obtained in terms of regularity, conorm, quadratic-conorm, and the geometric structure of the underlying Banach spaces.

Article information

Source
Adv. Oper. Theory, Volume 3, Number 1 (2018), 75-116.

Dates
Received: 31 March 2017
Accepted: 25 April 2017
First available in Project Euclid: 5 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.aot/1512497954

Digital Object Identifier
doi:10.22034/aot.1703-1149

Mathematical Reviews number (MathSciNet)
MR3730341

Zentralblatt MATH identifier
06804318

Subjects
Primary: 46L05: General theory of $C^*$-algebras
Secondary: 17C65: Jordan structures on Banach spaces and algebras [See also 46H70, 46L70] 46K70: Nonassociative topological algebras with an involution [See also 46H70, 46L70] 16U99: None of the above, but in this section 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 47D25 15A09: Matrix inversion, generalized inverses 46L60: Applications of selfadjoint operator algebras to physics [See also 46N50, 46N55, 47L90, 81T05, 82B10, 82C10] 47L30: Abstract operator algebras on Hilbert spaces

Keywords
C*-algebra partial isometry; von Neumann regularity Moore–Penrose invertibility JB*-triple tripotent reduced minimum modulus conorm quadraticconorm, extreme points

Citation

Fernández-Polo, Francisco J; Peralta, Antonio. Partial isometries: a survey. Adv. Oper. Theory 3 (2018), no. 1, 75--116. doi:10.22034/aot.1703-1149. https://projecteuclid.org/euclid.aot/1512497954


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