Density of the self-adjoint elements with finite spectrum in an irrational rotation C*-algebra.
Extremal Positive Semidefinite Forms.
Finite-rank perturbations of positive operators and isometries
We completely characterize the ranks of A - B and for operators A and B on a Hilbert space satisfying A ≥ B ≥ 0. Namely, let l and m be nonnegative integers or infinity. Then l = rank(A - B) and for some operators A and B with A ≥ B ≥ 0 on a Hilbert space of dimension n (1 ≤ n ≤ ∞) if and only if l = m = 0 or 0 < l ≤ m ≤ n. In particular, this answers in the negative the question posed by C. Benhida whether for positive operators A and B the finiteness of rank(A - B) implies that of . For...
Page 1