We study and compare the gap and the Riesz topologies of the space of all unbounded regular operators on Hilbert C*-modules. We show that the space of all bounded adjointable operators on Hilbert C*-modules is an open dense subset of the space of all unbounded regular operators with respect to the gap topology. The restriction of the gap topology on the space of all bounded adjointable operator...

We derive a spectral representation for the oblate spheroidal wave operator, which is holomorphic in the aspherical parameter Ω in a neighborhood of the real line. For real Ω, estimates are derived for all eigenvalue gaps uniformly in Ω. The proof of the gap estimates is based on detailed estimates for complex solutions of the Riccati equation. The spectral representation for complex Ω is deriv...

We determine the possible nonzero eigenvalues of compact selfadjoint operators A, B(1), B(2), . . ., B(m) with the property that A = B(1) +B(2) +· · ·+B(m). When all these operators are positive, the eigenvalues were known to be subject to certain inequalities which extend Horn’s inequalities from the finite-dimensional case when m = 2. We find the proper extension of the Horn inequalities and ...

Let S and T be linear operators in a linear space such that S ⊂ T . In this note an estimate for the codimension of domSn in domT n in terms of the codimension of domS in domT is obtained. An immediate consequence is that for any polynomial p the operator p(S) is a finite-dimensional restriction of the operator p(T ) whenever S is a finite-dimensional restriction of T . The general results are ...

where a(t, x, ξ) and b(t, x, ξ) are real symbols which are continuous in t and smooth with respect to x and ξ. The operator a(t, x,D) is selfadjoint; if b = 0 then this formally guarantees that the above evolution is L well-posed and the corresponding evolution operators S(t, s) are L isometries. The b term rougly contributes to the growth or decay of energy along the flow, depending on whether...