The Numerical Range of a Class of Self-adjoint Operator Functions

2007 ◽  
pp. 145-155
Author(s):  
Nurhan Çolakoglu
Keyword(s):  
Numerical Range ◽  
Adjoint Operator ◽  
Operator Functions

scholarly journals The block numerical range of analytic operator functions

2014 ◽  
pp. 901-934
Author(s):  
Agnes Radl ◽  
Christiane Tretter ◽  
Markus Wagenhofer
Keyword(s):  
Numerical Range ◽  
Analytic Operator ◽  
Operator Functions

scholarly journals Enclosure of the Numerical Range of a Class of Non-selfadjoint Rational Operator Functions

2017 ◽  
Vol 88 (2) ◽  
pp. 151-184 ◽  
Author(s):  
Christian Engström ◽  
Axel Torshage
Keyword(s):  
Numerical Range ◽  
Operator Functions

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 Numerical Ranges in II1 Factors

2017 ◽  
Vol 61 (1) ◽  
pp. 31-55
Author(s):  
Ken Dykema ◽  
Paul Skoufranis
Keyword(s):  
Convex Subset ◽  
Von Neumann Algebras ◽  
Numerical Range ◽  
Compact Convex ◽  
Adjoint Operator ◽  
Compact Convex Subset ◽  
Von Neumann

In this paper we generalize the notion of the C-numerical range of a matrix to operators in arbitrary tracial von Neumann algebras. For each self-adjoint operator C, the C-numerical range of such an operator is defined; it is a compact, convex subset of ℂ. We explicitly describe the C-numerical ranges of several operators and classes of operators.

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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