Perturbation of unbounded linear operators by $$\gamma $$ γ -relative boundedness

2017 ◽  
Vol 67 (2) ◽  
pp. 433-445
Author(s):  
Aymen Ammar ◽  
Faten Bouzayeni ◽  
Aref Jeribi
Keyword(s):  
Linear Operators ◽  
Unbounded Linear Operators

Unbounded Linear Operators

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Von Neumann ◽  
Limit Circle ◽  
Sectorial Operators ◽  
Closed Operators ◽  
The Stability ◽  
Symmetric Operators ◽  
Unbounded Linear Operators ◽  
Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

scholarly journals The numerical ranges of unbounded linear operators

1975 ◽  
Vol 12 (1) ◽  
pp. 23-25 ◽  
Author(s):  
Béla Bollobás ◽  
Stephan E. Eldridge
Keyword(s):  
Banach Space ◽  
Scalar Field ◽  
Banach Spaces ◽  
Unbounded Operator ◽  
Numerical Range ◽  
Linear Operators ◽  
Density Property ◽  
Unbounded Linear Operators

Giles and Joseph (Bull. Austral. Math. Soc. 11 (1974), 31–36), proved that the numerical range of an unbounded operator on a Banach space has a certain density property. They showed, in particular, that the numerical range of an unbounded operator on certain Banach spaces is dense in the scalar field. We prove that the numerical range of an unbounded operator on a Banach space is always dense in the scalar field.

Bounded and Unbounded Linear Operators

1987 ◽  
pp. 317-393 ◽  
Author(s):  
Vasile Ion Istrăţescu
Keyword(s):  
Linear Operators ◽  
Unbounded Linear Operators

Bounded and Unbounded Linear Operators

2011 ◽  
pp. 21-59
Author(s):  
Paul H. Bezandry ◽  
Toka Diagana
Keyword(s):  
Linear Operators ◽  
Unbounded Linear Operators

Approximately invariant subspaces for unbounded linear operators. II

1977 ◽  
Vol 227 (2) ◽  
pp. 177-182 ◽  
Author(s):  
Palle E. T. J�rgensen
Keyword(s):  
Invariant Subspaces ◽  
Linear Operators ◽  
Unbounded Linear Operators
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