scholarly journals Norm convergence of sectorial operators on varying Hilbert spaces

2013 ◽  
pp. 955-995 ◽  
Author(s):  
Delio Mugnolo ◽  
Robin Nittka ◽  
Olaf Post
Keyword(s):  
Hilbert Spaces ◽  
Norm Convergence ◽  
Sectorial 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 A quantitative mean ergodic theorem for uniformly convex Banach spaces

2009 ◽  
Vol 29 (6) ◽  
pp. 1907-1915 ◽  
Author(s):  
U. KOHLENBACH ◽  
L. LEUŞTEAN
Keyword(s):  
Banach Spaces ◽  
Ergodic Theorem ◽  
Hilbert Spaces ◽  
Local Stability ◽  
Uniformly Convex ◽  
Norm Convergence ◽  
Ergodic Averages ◽  
Mean Ergodic Theorem ◽  
Uniformly Convex Banach Spaces ◽  
The Mean

AbstractWe provide an explicit uniform bound on the local stability of ergodic averages in uniformly convex Banach spaces. Our result can also be viewed as a finitary version in the sense of Tao of the mean ergodic theorem for such spaces and so generalizes similar results obtained for Hilbert spaces by Avigad et al [Local stability of ergodic averages. Trans. Amer. Math. Soc. to appear] and Tao [Norm convergence of multiple ergodic averages for commuting transformations. Ergod. Th. & Dynam. Sys.28(2) (2008), 657–688].

Optimization of exact controllability for fractional impulsive partial stochastic differential systems via analytic sectorial operators

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Zuomao Yan ◽  
Yong-Hui Zhou
Keyword(s):  
Hilbert Spaces ◽  
Measure Of Noncompactness ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Exact Controllability ◽  
Differential Systems ◽  
New Class ◽  
Sectorial Operators ◽  
State Dependent ◽  
State Dependent Delay

AbstractIn this paper, we consider the optimization problems of exact controllability for a new class of fractional impulsive partial stochastic differential systems with state-dependent delay in Hilbert spaces. By utilizing suitable fixed point approach without imposing severe compactness condition on the operators, the theory of analytic sectorial operators, stochastic analysis, and the Hausdorff measure of noncompactness, some sufficient conditions are derived for achieving the required results. Finally, an example is provided to illustrate the obtained theory.

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