The Slater Condition in Infinite-Dimensional Vector Spaces

1980 ◽  
Vol 87 (6) ◽  
pp. 475 ◽  
Author(s):  
Jochem Zowe
Keyword(s):  
Vector Spaces ◽  
Dimensional Vector ◽  
Slater Condition ◽  
Infinite Dimensional

scholarly journals GROUP GRADINGS ON FINITARY SIMPLE LIE ALGEBRAS

2012 ◽  
Vol 22 (05) ◽  
pp. 1250046 ◽  
Author(s):  
YURI BAHTURIN ◽  
MATEJ BREŠAR ◽  
MIKHAIL KOCHETOV
Keyword(s):  
Abelian Group ◽  
Lie Algebras ◽  
Vector Spaces ◽  
Closed Field ◽  
Dimensional Vector ◽  
Linear Transformations ◽  
Special Linear ◽  
Infinite Dimensional ◽  
Group Gradings ◽  
Arbitrary Abelian Group

We classify, up to isomorphism, all gradings by an arbitrary abelian group on simple finitary Lie algebras of linear transformations (special linear, orthogonal and symplectic) on infinite-dimensional vector spaces over an algebraically closed field of characteristic different from 2.

scholarly journals Localization and computation in an approximation of eigenvalues

Filomat ◽  
2015 ◽  
Vol 29 (1) ◽  
pp. 75-81
Author(s):  
S.V. Djordjevic ◽  
G. Kantún-Montiel
Keyword(s):  
Hilbert Spaces ◽  
Finite Rank ◽  
Vector Spaces ◽  
Dimensional Case ◽  
Dimensional Vector ◽  
Infinite Dimensional ◽  
Weyl Spectrum ◽  
Isolated Points ◽  
Isolated Point ◽  
Different Parts

In this note we consider the problem of localization and approximation of eigenvalues of operators on infinite dimensional Banach and Hilbert spaces. This problem has been studied for operators of finite rank but it is seldom investigated in the infinite dimensional case. The eigenvalues of an operator (between infinite dimensional vector spaces) can be positioned in different parts of the spectrum of the operator, even it is not necessary to be isolated points in the spectrum. Also, an isolated point in the spectrum is not necessary an eigenvalue. One method that we can apply is using Weyl?s theorem for an operator, which asserts that every point outside the Weyl spectrum is an isolated eigenvalue.

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