Diagonals of self-adjoint operators
By W. Arveson, R. Kadison. 2005
76 citations recorded by the source corpus.
The eigenvalues of a self-adjoint nxn matrix A can be put into a decreasing sequence $\lambda=(\lambda_1,...,\lambda_n)$, with repetitions according to multiplicity, and the diagonal of A is a point of $R^n$ that bears some relation to $\lambda$. The Schur-Horn theorem characterizes that relation in terms of a system of linear inequalities. We give a new proof of the latter result for positive trace-class operators on infinite dimensional Hilbert spaces, generalizing results of one of us on the diagonals of projections. We also establish an appropriate counterpart of the Schur inequalities that relate spectral properties of self-adjoint operators in $II_1$ factors to their images under a conditional expectation onto a maximal abelian subalgebra.
Subfields: Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1dc3b4858c2e20dd58425e0ea1ce4ba98d659cb2
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In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- An infinite dimensional Schur-Horn theorem and majorization theory with applications to operator ideals (2007, methodology): “(ii) The equivalence of (i) and (iv) was proven by Arveson and Kadison in [3, Theorem 4.2] In the case of finite rank positive operators, the “sequence” formulation S(i)⇔S(ii′) in the above corollary is obviously equivalent to the operator theory formulation of the classical Schur-Horn Theorem (see ”
- THE SCHUR-HORN THEOREM FOR OPERATORS AND FRAMES WITH PRESCRIBED NORMS AND FRAME OPERATOR. (2005, result): “Related results can be found in R. Kadison [14], [15], and Arveson and Kadison [ 2 ] (which appeared during the revision process of this work).”