Let E be a Banach lattice, T be a bounded operator on E. The Weyl essential spectrum σew(T ) of the operator T is a set σew(T ) = ∩ K∈K(E) σ(T + K), where K(E) is a set of all compact operators on E. In particular for a positive operator T next subsets of the spectrum

We study the adjointness problem for the closed extensions of a general b-elliptic operator A ∈ x Diffmb (M ;E), ν > 0, initially defined as an unbounded operator A : C∞ c (M ;E) ⊂ x L b (M ;E) → xL b (M ;E), μ ∈ R. The case where A is a symmetric semibounded operator is of particular interest, and we give a complete description of the domain of the Friedrichs extension of such an operator.

Communicated by Abstract. We will prove that, if every finite dimensional subspace of an infinite dimensional operator space E is 1-completely complemented in it, E is 1-Hilbertian and 1-homogeneous. However, this is not true for finite dimensional operator spaces: we give an example of an n-dimensional operator space E, such that all of its subspaces are 1-completely complemented in E, but whi...

This is work in progress with Yael Karshon. We develop a localization formula in equivariant cohomology which generalizes both the classical Duistermaat-Heckman formula and the localization formula of Paradan and Woodward for the norm-square of the moment map. Applying a case of our formula to a toric variety, we recover the classical Brianchon-Gram decomposition of a polytope, thus answering a...

Let E be a natural operator associated to the curvature tensor of a pseudo-Riemannian manifold. We study when the spectrum, or more generally the real Jordan normal form, of E is constant on the natural domain of definition. In particular, we examine the Jacobi operator, the higher order Jacobi operator, the Szabo operator, and the skew-symmetric curvature operator.

In this paper, an iterative method is proposed for solving large general Sylvester matrix equation $AXB+CXD = E$, where $A in R^{ntimes n}$ , $C in R^{ntimes n}$ , $B in R^{stimes s}$ and  $D in R^{stimes s}$ are given matrices and $X in R^{stimes s}$  is the unknown matrix. We present a global conjugate gradient (GL-CG) algo- rithm for solving linear system of equations with multiple right-han...

There is a widespread belief in the quantum physical community, and in textbooks used to teach Quantum Mechanics, that it is a difficult task to apply the time evolution operator e itˆH / on an initial wave function. That is to say, because the hamiltonian operator generally is the sum of two operators, then it is a difficult task to apply the time evolution operator on an initial wave function...

De nition. Let (V, 〈 , 〉) be a n-dimensional euclidean vector space and T : V −→ V a linear operator. We will call the adjoint of T , the linear operator S : V −→ V such that: 〈T (u), v〉 = 〈u, S(v)〉 , for all u, v ∈ V . Proposition 1. Let (V, 〈 , 〉) be a n-dimensional euclidean vector space and T : V −→ V a linear operator. The adjoint of T exists and is unique. Moreover, if E denotes an orthon...

We study the extension of linear operators with range in a C(K)space, comparing and contrasting our results with the corresponding results for the nonlinear problem of extending Lipschitz maps with values in a C(K)space. We give necessary and sufficient conditions on a separable Banach space X which ensure that every operator T : E → C(K) defined on a subspace may be extended to an operator e T...