Variational Principles for Eigenvalues of Self-adjoint Operator Functions

2004 ◽  
Vol 49 (3) ◽  
pp. 287-321 ◽  
Author(s):  
David Eschw� ◽  
Matthias Langer
Keyword(s):  
Variational Principles ◽  
Adjoint Operator ◽  
Operator Functions

scholarly journals Triple variational principles for self-adjoint operator functions

2016 ◽  
Vol 270 (6) ◽  
pp. 2019-2047 ◽  
Author(s):  
Matthias Langer ◽  
Michael Strauss
Keyword(s):  
Variational Principles ◽  
Adjoint Operator ◽  
Operator Functions

Variational principles for real eigenvalues of self-adjoint operator pencils

2000 ◽  
Vol 38 (2) ◽  
pp. 190-206 ◽  
Author(s):  
Paul Binding ◽  
David Eschw� ◽  
Heinz Langer
Keyword(s):  
Variational Principles ◽  
Adjoint Operator ◽  
Operator Pencils

scholarly journals COMMUTATOR ESTIMATES AND $\RR$-FLOWS IN NON-COMMUTATIVE OPERATOR SPACES

2007 ◽  
Vol 50 (2) ◽  
pp. 293-324 ◽  
Author(s):  
Ben de Pagter ◽  
Fyodor Sukochev
Keyword(s):  
Symmetric Operator ◽  
Von Neumann Algebra ◽  
Adjoint Operator ◽  
Operator Spaces ◽  
Von Neumann ◽  
Finite Von Neumann Algebra ◽  
Operator Functions ◽  
Strongly Continuous Groups ◽  
Symmetric Operator Spaces ◽  
Groups Of Isometries

AbstractThe principal results in this paper are concerned with the description of domains of infinitesimal generators of strongly continuous groups of isometries in non-commutative operator spaces $E(\mathcal{M},\tau)$, which are induced by $\mathbb{R}$-flows on $\mathcal{M}$. In particular, we are concerned with the description of operator functions which leave the domain of such generators invariant in all symmetric operator spaces, associated with a semi-finite von Neumann algebra $\mathcal{M}$ and a separable function space $E$ on $(0,\infty)$. Furthermore, we apply our results to the study of operator functions for which $[D,x]\in E(\mathcal{M},\tau)$ implies that $[D,f(x)]\in E(\mathcal{M},\tau)$, where $D$ is an unbounded self-adjoint operator. Our methods are partly based on the recently developed theory of double operator integrals in symmetric operator spaces and the theory of adjoint $C_{0}$-semigroups.

scholarly journals Variational characterizations for eigenfunctions of analytic self-adjoint operator functions

2013 ◽  
Vol 33 (2) ◽  
pp. 307 ◽  
Author(s):  
Georgis Katsouleas ◽  
John Maroulas
Keyword(s):  
Adjoint Operator ◽  
Operator Functions
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