We introduce and investigate the orbit-closed $C$-numerical range, a natural modification of range an operator introduced for $C$ trace-class by Dirr vom Ende. Our is conservative theirs because these two sets have same closure even coincide when finite rank. Since Ende's results concerning depend only on its closure, our inherits properties, but we also establish more. For selfadjoint, Ende we...

LetH be a Hilbert space, L(H) the algebra of all bounded linear operators onH and 〈, 〉A : H ×H → C the bounded sesquilinear form induced by a selfadjoint A ∈ L(H), 〈ξ, η〉A = 〈Aξ, η〉 , ξ, η ∈ H. Given T ∈ L(H), T is A-selfadjoint if AT = T A. If S ⊆ H is a closed subspace, we study the set of A-selfadjoint projections onto S, P(A,S) = {Q ∈ L(H) : Q = Q , R(Q) = S , AQ = QA} for different choices...

This paper touches upon several traditional topics of 1D linear complex analysis including distribution of zeros of entire functions, completeness problem for complex exponentials and for other families of special functions, some problems of spectral theory of selfadjoint differential operators. Their common feature is the close relation to the theory of complex Fourier transform of compactly s...

Consider a selfadjoint unbounded operator D on a Hilbert space H and a one parameter norm continuous family of selfadjoint bounded operators {A(t) | t ∈ R} that converges in norm to asymptotes A± at ±∞. Then under certain conditions [RoSa95] that include the assumption that the operators {D(t) = D + A(t), t ∈ R} all have discrete spectrum then the spectral flow along the path {D(t)} can be show...

For a class of bounded random selfadjoint operators (Lu)(n) =

We consider the Dirac equation with a magnetic-solenoid field (the superposition of a solenoid field and a collinear uniform magnetic field). Using von Neumann’s theory of the selfadjoint extensions of symmetric operators, we construct selfadjoint Dirac Hamiltonians for the case of the Aharonov-Bohm solenoid in 2 + 1 and 3 + 1 dimensions. Each extension of the family is specified by certain asy...