Noncompact Lie‐algebraic approach to the unitary representations of SU∼(1,1): Role of the confluent hypergeometric equation

1974 ◽  
Vol 15 (3) ◽  
pp. 380-382 ◽  
Author(s):  
W. Montgomery ◽  
L. O'Raifeartaigh
Keyword(s):  
Algebraic Approach ◽  
Unitary Representations ◽  
Hypergeometric Equation ◽  
Confluent Hypergeometric Equation

The role of the algebraic structure in Wold-type decomposition

2021 ◽  
Vol 33 (4) ◽  
pp. 1033-1049
Author(s):  
G. A. Bagheri Bardi ◽  
Zbigniew Burdak ◽  
Akram Elyaspour
Keyword(s):  
Linear Algebra ◽  
Algebraic Structure ◽  
Von Neumann Algebras ◽  
Algebraic Approach ◽  
Von Neumann ◽  
Weak Operator ◽  
Commuting Pairs ◽  
Decomposition Theorems ◽  
Type Decomposition

Abstract In recent works [G. A. Bagheri-Bardi, A. Elyaspour and G. H. Esslamzadeh, Wold-type decompositions in Baer ∗ \ast -rings, Linear Algebra Appl. 539 2018, 117–133] and [G. A. Bagheri-Bardi, A. Elyaspour and G. H. Esslamzadeh, The role of algebraic structure in the invariant subspace theory, Linear Algebra Appl. 583 2019, 102–118], the algebraic analogues of the three major decomposition theorems of Wold, Nagy–Foiaş–Langer and Halmos–Wallen were established in the larger category of Baer * {*} -rings. The results have their versions for commuting pairs in von Neumann algebras. In the corresponding proofs, both norm and weak operator topologies are heavily involved. In this work, ignoring topological structures, we give an algebraic approach to obtain them in Baer * {*} -rings.

Sign in / Sign up

Export Citation Format

Share Document