SELF-ADJOINT OPERATORS IN INDEFINITE INNER PRODUCT SPACES

1988 ◽  
Vol 39 (3) ◽  
pp. 333-348
Author(s):  
K. C. HANNABUSS
Keyword(s):  
Inner Product ◽  
Product Spaces ◽  
Indefinite Inner Product ◽  
Inner Product Spaces ◽  
Adjoint Operators

scholarly journals Classification of linear mappings between indefinite inner product spaces

2017 ◽  
Vol 531 ◽  
pp. 356-374 ◽  
Author(s):  
Juan Meleiro ◽  
Vladimir V. Sergeichuk ◽  
Thiago Solovera ◽  
André Zaidan
Keyword(s):  
Inner Product ◽  
Product Spaces ◽  
Indefinite Inner Product ◽  
Inner Product Spaces

Self-adjoint operators on inner product spaces over fields of power series

2008 ◽  
Vol 58 (4) ◽  
Author(s):  
Hans Keller ◽  
Ochsenius Herminia
Keyword(s):  
Power Series ◽  
Adjoint Operator ◽  
Inner Product ◽  
Closed Field ◽  
Product Spaces ◽  
Binary Forms ◽  
Inner Product Spaces ◽  
Finite Dimensional ◽  
Orthogonal Decompositions ◽  
Adjoint Operators

AbstractTheorems on orthogonal decompositions are a cornerstone in the classical theory of real (or complex) matrices and operators on ℝn. In the paper we consider finite dimensional inner product spaces (E, ϕ) over a field K = F((χ 1, ..., x m)) of generalized power series in m variables and with coefficients in a real closed field F. It turns out that for most of these spaces (E, ϕ) every self-adjoint operator gives rise to an orthogonal decomposition of E into invariant subspaces, but there are some salient exceptions. Our main theorem states that every self-adjoint operator T: (E, ϕ) → (E, ϕ) is decomposable except when dim E is a power of 2 with exponent at most m, and ϕ is a tensor product of pairwise inequivalent binary forms. In the exceptional cases we provide an explicit description of indecomposable operators.

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