منابع مشابه
Diagonals of Self-adjoint Operators
The eigenvalues of a self-adjoint 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 that bears some relation to λ. The Schur-Horn theorem characterizes that relation in terms of a system of linear inequalities. We prove an extension of the latter result for positive trace-class operators on ...
متن کاملA Characterization of Positive Self-adjoint Extensions and Its Application to Ordinary Differential Operators
A new characterization of the positive self-adjoint extensions of symmetric operators, T0, is presented, which is based on the Friedrichs extension of T0, a direct sum decomposition of domain of the adjoint T ∗ 0 and the boundary mapping of T ∗ 0 . In applying this result to ordinary differential equations, we characterize all positive self-adjoint extensions of symmetric regular differential o...
متن کاملMultilinear Interpolation between Adjoint Operators
Multilinear interpolation is a powerful tool used in obtaining strong type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear operator satisfies a weak L estimate for a single index q (which may be less than one) and that all the adjoints of the multilinear operator are of similar natu...
متن کاملNon-self-adjoint Differential Operators
We describe methods which have been used to analyze the spectrum of non-self-adjoint differential operators, emphasizing the differences from the self-adjoint theory. We find that even in cases in which the eigenfunctions can be determined explicitly, they often do not form a basis; this is closely related to a high degree of instability of the eigenvalues under small perturbations of the opera...
متن کاملAdjoints and Self-Adjoint Operators
Let V and W be real or complex finite dimensional vector spaces with inner products 〈·, ·〉V and 〈·, ·〉W , respectively. Let L : V → W be linear. If there is a transformation L∗ : W → V for which 〈Lv,w〉W = 〈v, Lw〉V (1) holds for every pair of vectors v ∈ V and w in W , then L∗ is said to be the adjoint of L. Some of the properties of L∗ are listed below. Proposition 1.1. Let L : V →W be linear. ...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 1990
ISSN: 0893-9659
DOI: 10.1016/0893-9659(90)90127-w