BRANKO CURGUS and BRANKO NAJMAN Deenitizable operators in Krein spaces have spectral properties similar to those of selfadjoint operators in Hilbert spaces. A suucient condition for deenitizability of a selfadjoint operator A with a nonempty resolvent set (A) in a Krein space (H; j ]) is the niteness of the number of negative squares of the form Axjy] (see 10, p. 11]). In this note we consider ...

s[v] = preo[v] s[w] = prvo[w] ∀w ∈ vars(prvo) s[Ov] = o s[Ow] = frozen ∀w ∈ vars(prvo) s[Cw] = v ∀w ∈ vars(prvo) We show that all operators o′ that interfere with Fire(o) are not applicable in s. Thus Fire(o) is the only applicable operator in Ts. Second, we show that for all these operators o′ ∈ Ts (except for Fire(o)), Ts already contains a necessary enabling set for o′ in s. Let u 6= Fire(o)...

A general procedure is derived for obtaining sufficient conditions for the similarity of operators T and T + P. This is applied to obtain sharp conditipns for the similarity of the Volterra operators J: f(x)-+ / f(y)dy and J + P where P: f(x) /+/fp(x,y)f(y)dy. By the same methods perturbations of the one sided shift operator S on LP(Ofo) by certain trace class operators P are shown to be simila...

For each S ∈ L(E) (with E a Banach space) the operator R(S) ∈ L(E/E) is defined by R(S)(x + E) = Sx + E (x ∈ E). We study mapping properties of the correspondence S → R(S), which provides a representation R of the weak Calkin algebra L(E)/W (E) (here W (E) denotes the weakly compact operators on E). Our results display strongly varying behaviour of R. For instance, there are no non–zero compact...

Denote by W (A) the numerical range of a bounded linear operator A, and [A, B] = AB −BA the Lie product of two operators A and B. Let H, K be complex Hilbert spaces of dimension ≥ 2 and Φ : B(H) → B(K) be a map whose range contains all operators of rank ≤ 1. It is shown that Φ satisfies that W ([Φ(A), Φ(B)]) = W ([A, B]) for any A, B ∈ B(H) if and only if dim H = dim K, there exist ε ∈ {1,−1}, ...

Common estimation algorithms, such as least squares estimation or the Kalman filter, operate on a state in a state space S that is represented as a real-valued vector. However, for many quantities, most notably orientations in 3D, S is not a vector space, but a so-called manifold, i.e. it behaves like a vector space locally but has a more complex global topological structure. For integrating th...

Given a semidirect product g = s ⊎ r of semisimple Lie algebras s and solvable algebras r, we construct polynomial operators in the enveloping algebra U(g) of g that commute with r and transform like the generators of s, up to a functional factor that turns out to be a Casimir operator of r. Such operators are said to generate a virtual copy of s in U(g), and allow to compute the Casimir operat...

Elastic wave propagation in anisotropic media is well represented by elastic wave equations. Modeling based on elastic wave equations characterizes both kinematics and dynamics correctly. However, because P and S modes are both propagated using elastic wave equations, there is a need to separate P and S modes to obtain clean elastic images. The separation of wave modes to P and S from isotropic...

in this paper we study properties of symbols such that these belong to class of symbols sitting insidesm ρ,φ that we shall introduce as the following. so for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of m−hypoelliptic pseudodifferential operators for which define base on this class of symbols. also we consider maxi...

We introduce a class of pseudodifferential operators in the anisotropic setting induced by an expansive dilation A which generalizes the classical isotropic class S γ,δ of inhomogeneous symbols. We extend a well-known L -boundedness result to the anisotropic class S δ,δ(A), 0 ≤ δ < 1. As a consequence, we deduce that operators with symbols in the anisotropic class S 1,0(A) are bounded on L p sp...