a project to characterize diagonals of operators, especially selfadjoint operators, in terms of spectral data.
We provide a survey of the current state of the study of diagonals of operators, especially selfadjoint operators. In addition, we provide a few new results made possible by recent work of Müller--Tomilov and Kaftal--Loreaux. This is an expansion of …
Kadison characterized the diagonals of projections and observed the presence of an integer, which Arveson later recognized as a Fredholm index obstruction applicable to any normal operator with finite spectrum coincident with its essential spectrum …
As applications of Kadison's Pythagorean and carpenter's theorems, the Schur–Horn theorem, and Thompson's theorem, we obtain an extension of Thompson's theorem to compact operators and use these ideas to give a characterization of diagonals of …
Kadison's Pythagorean theorem (2002) provides a characterization of the diagonals of projections with a subtle integrality condition. Arveson (2007), Kaftal, Ng, Zhang (2009), and Argerami (2015) all provide different proofs of that integrality …
We prove that a nonzero idempotent is zero-diagonal if and only if it is not a Hilbert–Schmidt perturbation of a projection, along with other useful equivalences. Zero-diagonal operators are those whose diagonal entries are identically zero in some …
Schur–Horn theorems focus on determining the diagonal sequences obtainable for an operator under all possible basis changes, formally described as the range of the canonical conditional expectation of its unitary orbit. Following a brief background …