On unitary invariance of some classes of operators in Hilbert spaces

2020 ◽  
Vol 9 (1) ◽  
pp. 45-52
Author(s):  
Linety N. Muhati ◽  
J. M. Khalagai
Keyword(s):  
Hilbert Spaces ◽  
Unitary Invariance

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.

On the Sum of Generalized Frames in Hilbert Spaces

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
F. Abtahi ◽  
Z. Kamali ◽  
Z. Keyshams
Keyword(s):  
Hilbert Spaces
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