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Selfadjoint Operators and Cones
 J. London Math. Soc
"... Suppose that K is a cone in a real Hilbert space H with K ? = f0g and that A : H ! H is a selfadjoint operator which maps K into itself. If kAk is an eigenvalue of A, it is shown that it has an eigenvector in the cone. As a corollary it follows that if k A k n is an eigenvalue of A n then ..."
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Suppose that K is a cone in a real Hilbert space H with K ? = f0g and that A : H ! H is a selfadjoint operator which maps K into itself. If kAk is an eigenvalue of A, it is shown that it has an eigenvector in the cone. As a corollary it follows that if k A k n is an eigenvalue of A n
Diagonals of selfadjoint operators
"... Abstract. The eigenvalues of a selfadjoint n×n matrix A can be put into a decreasing sequence λ = (λ1,..., λn), with repetitions according to multiplicity, and the diagonal of A is a point of R n that bears some relation to λ. The SchurHorn theorem characterizes that relation in terms of a system ..."
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properties of selfadjoint operators in II1 factors to their images under a conditional expectation onto a maximal abelian subalgebra. 1. Preface These are research notes that are not intended for publication in their present form. They summarize some of the results of a project begun by the authors
NonSelfAdjoint Operators and
, 2006
"... The theory of pseudospectra has grown rapidly since its emergence from within numerical analysis around 1990. We describe some of its applications to the stability theory of differential operators, to WKB analysis and even to orthogonal polynomials. Although currently more a way of looking at nonse ..."
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The theory of pseudospectra has grown rapidly since its emergence from within numerical analysis around 1990. We describe some of its applications to the stability theory of differential operators, to WKB analysis and even to orthogonal polynomials. Although currently more a way of looking at nonselfadjoint
OF SELFADJOINT OPERATORS ∗
, 2013
"... The absolute change in the Rayleigh quotient (RQ) is bounded in this paper in terms of the norm of the residual and the change in the vector. If x is an eigenvector of a selfadjoint bounded operator A in a Hilbert space, then the RQ of the vector x, denoted by (x), is an exact eigenvalue of A. In t ..."
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The absolute change in the Rayleigh quotient (RQ) is bounded in this paper in terms of the norm of the residual and the change in the vector. If x is an eigenvector of a selfadjoint bounded operator A in a Hilbert space, then the RQ of the vector x, denoted by (x), is an exact eigenvalue of A
Selfadjoint operators on surfaces in R
 n , Differential Geom. Appl. Vol
"... Our aim in this paper is to define principal and characteristic directions at points on a smooth 2dimensional surface in the Euclidean space R 4 in such a way that their equations together with that of the asymptotic directions behave in the same way as the triple formed by their counterpart on smo ..."
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on smooth surfaces in the Euclidean space R 3. The definitions we propose are derived from a more general approach, namely an analysis of selfadjoint operators on 2dimensional smooth surfaces in the Euclidean space R n. 1
EXPONENTIAL ORDERING ON BOUNDED SELFADJOINT OPERATORS
"... Abstract. Reducibility property is proved for bounded selfadjoint operators satisfying the exponential ordering. ..."
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Abstract. Reducibility property is proved for bounded selfadjoint operators satisfying the exponential ordering.
Spectral Theory for Bounded Selfadjoint Operators
"... Spectral theory for a selfadjoint operator is a quite complicated topic. If the operator at hand is compact the theory becomes, if not trivial, less complicated. Consider first the case of a selfadjoint operator A: V → V with V finite dimensional. The complete spectral decomposition of A can ..."
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Spectral theory for a selfadjoint operator is a quite complicated topic. If the operator at hand is compact the theory becomes, if not trivial, less complicated. Consider first the case of a selfadjoint operator A: V → V with V finite dimensional. The complete spectral decomposition of A can
Ergodic semigroups of positivity preserving selfadjoint operators
 J. FUNCT. ANAL
, 1973
"... We prove that an ergodic semigroup of positivity preserving selfadjoint operators is positivity improving. We also present a new proof (using Markov techniques) of the ergodicity of semigroups generated by spatially cutoff P(y)% Hamiltonians. ..."
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We prove that an ergodic semigroup of positivity preserving selfadjoint operators is positivity improving. We also present a new proof (using Markov techniques) of the ergodicity of semigroups generated by spatially cutoff P(y)% Hamiltonians.
Results 1  10
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65,725