Towards a non-selfadjoint version of Kadison’s theorem

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Constructive Proof of the Carpenter’s Theorem

We give a constructive proof of Carpenter’s Theorem due to Kadison [14, 15]. Unlike the original proof our approach also yields the real case of this theorem. 1. Kadison’s theorem In [14] and [15] Kadison gave a complete characterization of the diagonals of orthogonal projections on a Hilbert space H. Theorem 1.1 (Kadison). Let {di}i∈I be a sequence in [0, 1]. Define a = ∑ di<1/2 di and b = ∑ d...

Non-selfadjoint matrix Sturm-Liouville operators with eigenvalue-dependent boundary conditions

In this paper we investigate discrete spectrum of the non-selfadjoint matrix Sturm-Liouville operator L generated in L (R+, S) by the differential expression ` (y) = −y +Q (x) y , x ∈ R+ : [0,∞) , and the boundary condition y′ (0)− ( β0 + β1λ+ β2λ 2 ) y (0) = 0 where Q is a non-selfadjoint matrix valued function. Also using the uniqueness theorem of analytic functions we prove that L has a fini...

A More General Version of the Costa Theorem

In accordance with the Costa theorem, the interference which is independent of the channel input and known non-causally at the transmitter, does not affect the capacity of the Gaussian channel. In some applications, the known interference depends on the input and hence has some information. In this paper, we study the channel with input dependent interference and prove a capacity theorem that n...

The Schur-horn Theorem for Operators with Finite Spectrum

We characterize the set of diagonals of the unitary orbit of a self-adjoint operator with a finite spectrum. Our result extends the Schur-Horn theorem from a finite dimensional setting to an infinite dimensional Hilbert space, analogous to Kadison’s theorem for orthogonal projections [17, 18], and the second author’s result for operators with three point spectrum [16].