The spectral properties of a certain class of self-adjoint operator functions

1974 ◽  
Vol 8 (1) ◽  
pp. 1-9 ◽  
Author(s):  
A. I. Virozub ◽  
V. I. Matsaev
Keyword(s):  
Spectral Properties ◽  
Adjoint Operator ◽  
Operator Functions

scholarly journals Spectral Enclosures and Complex Resonances for General Self-Adjoint Operators

1998 ◽  
Vol 1 ◽  
pp. 42-74 ◽  
Author(s):  
E.B. Davies
Keyword(s):  
Spectral Properties ◽  
Linear Subspace ◽  
Adjoint Operator ◽  
Dimensional Linear Subspace ◽  
Finite Dimensional ◽  
Adjoint Operators ◽  
Computation Of Eigenvalues

AbstractThis paper considers a number of related problems concerning the computation of eigenvalues and complex resonances of a general self-adjoint operator H. The feature which ties the different sections together is that one restricts oneself to spectral properties of H which can be proved by using only vectors from a pre-assigned (possibly finite-dimensional) linear subspace L.

Spectral properties of cosine operator functions

1988 ◽  
Vol 36 (1) ◽  
pp. 80-98 ◽  
Author(s):  
Ioana Cioranescu ◽  
Carlos Lizama
Keyword(s):  
Spectral Properties ◽  
Cosine Operator ◽  
Operator Functions ◽  
Cosine Operator Functions

scholarly journals Spectral properties of singular Sturm—Liouville operators with indefinite weight sgn x

2009 ◽  
Vol 139 (3) ◽  
pp. 483-503 ◽  
Author(s):  
Illya Karabash ◽  
Carsten Trunk
Keyword(s):  
Critical Point ◽  
Spectral Properties ◽  
Krein Space ◽  
Adjoint Operator ◽  
Real Spectrum ◽  
Real Point ◽  
Indefinite Weight ◽  
Sturm Liouville ◽  
Regular Critical Point ◽  
Liouville Operators

We consider a singular Sturm—Liouville expression with the indefinite weight sgn x. There is a self-adjoint operator in some Krein space associated naturally with this expression. We characterize the local definitizability of this operator in a neighbourhood of ∞. Moreover, in this situation, the point ∞ is a regular critical point. We construct an operator A = (sgn x)(−d2/dx2 + q) with non-real spectrum accumulating to a real point. The results obtained are applied to several classes of Sturm—Liouville operators.

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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