Geršgorin theory and the definiteness of determinantal operators

1987 ◽  
Vol 106 (1-2) ◽  
pp. 1-10 ◽  
Author(s):  
D. R. Farenick ◽  
Patrick J. Browne
Keyword(s):  
Spectral Theory ◽  
Hilbert Spaces ◽  
Diagonal Dominance ◽  
Dominance Properties

SynopsisLet Aij, l≦j≦k, be bounded Hermitean operators on Hilbert spaces Hi, 1≦i≦k, and let be the induced operators on . An important operator for multiparameter theory is δ: H →H denned by δ = det the determinant being expanded formally. Various definiteness properties of δ are critical for multiparameter spectral theory.We use the operators Aij to construct a numerical matrix δ(δ) upon which we use Geršgorin theory to investigate the non-singularity and definiteness of δ. Diagonal dominance properties of the array [Aij] are also discussed.

scholarly journals Some Properties of Spectral Theory in Fuzzy Hilbert Spaces

2017 ◽  
Vol 8 (2) ◽  
pp. 1-7
Author(s):  
Noori F. Al-Mayahi ◽  
Abbas M. Abbas
Keyword(s):  
Linear Operator ◽  
Spectral Theory ◽  
Hilbert Spaces ◽  
Normed Spaces

In this paper we give some definitions and properties of spectral theory in fuzzy Hilbert spaces also we introduce  definitions Invariant  under a linear operator  on fuzzy normed spaces and reduced  linear operator on fuzzy Hilbert spaces and we prove theorms  related to eigenvalue and eigenvectors ,eigenspace in fuzzy normed , Invariant and  reduced in fuzzy Hilbert spaces  and  show relationship between them.

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