scholarly journals Generalized Eigenspaces and the Jordan Decomposition

2020 ◽  
pp. 1-62
Keyword(s):  
Jordan Decomposition

Multiplicative Jordan Decomposition in Group Rings of 3-Groups, II

2014 ◽  
Vol 42 (6) ◽  
pp. 2633-2639 ◽  
Author(s):  
Chia-Hsin Liu ◽  
D. S. Passman
Keyword(s):  
Group Rings ◽  
Jordan Decomposition

Orthomorphisms of archimedean vector lattices

1981 ◽  
Vol 89 (1) ◽  
pp. 119-128 ◽  
Author(s):  
S. J. Bernau
Keyword(s):  
Linear Operator ◽  
Vector Lattice ◽  
Jordan Decomposition ◽  
Duality Results ◽  
Vector Lattices ◽  
Elementary Methods ◽  
Disjointness Preserving ◽  
Order Boundedness

AbstractA linear operator T on a vector lattice L preserves disjointness if Tx ⊥ y whenever x ⊥ y. If such a T is positive it is automatically order bounded. An ortho-morphism is an order bounded disjointness preserving linear operator on L. In this note we show that the theory of orthomorphisms on archimedean vector lattices admits a totally elementary exposition. Elementary methods are also effective in duality considerations when the order dual separates points of L. For the Jordan decomposition T = T+ − T− with T+x = (Tx+)+ − (Tx−)+ we can dtrop the order boundedness assumption if we assume either that T preserves ideals or that L is normed and T is continuous. Alternatively we may keep order boundedness and assume only |Tx| ⊥ |Ty| whenever x ⊥ y. The main duality results show: T preserves ideals if and only if T** does; T is an orthomorphism if and only if T* is; T is central (|T| is bounded by a multiple of the identity) if and only if T* is central if and only if T and T* preserve ideals.

Hahn-Jordan decomposition for smooth measures

1981 ◽  
Vol 30 (3) ◽  
pp. 710-712
Author(s):  
E. T. Shavgulidze
Keyword(s):  
Jordan Decomposition ◽  
Smooth Measures
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