For a bounded linear operator A on a Banach space we characterize the isolated points in the spectrum of A , the Riesz points of A , and the poles of the resolvent of A . 1. Terminology and introduction Throughout this paper E will be an infinite-dimensional complex Banach space and A will be a bounded linear operator on E. We denote by N(A) the kernel and by A(E) the range of A. The spectrum o...

LEARNING PROCEDURAL PLANNING KNOWLEDGE IN COMPLEX ENVIRONMENTS by Douglas John Pearson Chair: John E. Laird In complex, dynamic environments, an agent's knowledge of the environment (its domain knowledge) will rarely be complete and correct. Existing approaches to learning and correcting domain knowledge have focused on either learning procedural knowledge to directly guide execution (e.g. rein...

and Applied Analysis 3 Krein-Rutman theorem see 34 , we infer that if r B / 0, then there exist φ ∈ P \ {θ} and g∗ ∈ P ∗ \ {θ} such that Bφ r B φ, B∗g∗ r B g∗. 2.1 For a given constant δ > 0, set P ( g∗, δ ) { x ∈ P, g∗ x ≥ δ‖x‖, 2.2 then P g∗, δ is also a cone in E. Definition 2.1 see 30 . Let D ⊂ E and F : D → E a nonlinear operator. F is said to be quasiadditive on lattice, if there exists y...

Ž . Chaos quantization conditions, which relate the eigenvalues of a Hermitian operator the Riemann operator with the non-trivial zeros of the Riemann zeta function are considered, and their geometrical interpretation is discussed. q 1999 Published by Elsevier Science B.V. All rights reserved. PACS: 11.25.M; 05.45.M; 02.10.L For a long time a challenge for mathematical physics has been and is s...

This paper investigates the pseudospectra and the numerical range of the OrrSommerfeld operator for plane Poiseuille flow. A number z E C is in the E-pseudospectrum of a matrix or operator A if Il(zI A)-'II 2 E-l, or, equivalently, if z is in the spectrum of A + E for some perturbation E satisfying IlEll 5 E. The numerical range of A is the set of numbers of the form (Au, u), where (., .) is th...

Rayleigh Schrodinger perturbation expansion is applied to the system where the unperturbed Hamiltonian Ho is chosen to be an alternant operator, while the perturbation J.. V is chosen to be an antialternant operator. A configuration interaction space X .. generated by n electrons moving over 2n orthonormalised orbitals is considered. This space splits into two mutually complementary subspaces x...

The paper is a concise survey of some rigorous results on the Fox–Li operator. This operator may be interpreted as a large truncation of a Wiener–Hopf operator with an oscillating symbol. Employing theorems from Wiener–Hopf theory one can therefore derive remarkable properties of the Fox–Li operator in a fairly comfortable way, but it turns out that Wiener–Hopf theory is unequal to the task of ...

In analogy with the maximal tensor product of C-algebras, we deene the \maximal" tensor product E 1 E 2 of two operator spaces E 1 and E 2 and we show that it can be identiied completely isometrically with the sum of the two Haagerup tensor We also study the extension to more than two factors.

In analogy with the maximal tensor product of C *-algebras, we define the " maximal " tensor product E 1 ⊗ µ E 2 of two operator spaces E 1 and E 2 and we show that it can be identified completely isometrically with the sum of the two Haagerup tensor

Let M be a compact Riemannian manifold with an action by isometries of a compact Lie group G. Suppose that this action could be lifted to an action by isometries on a Clifford bundle E over M. We use the method of the Witten deformation to compute the virtual representation-valued index of a transversally elliptic Dirac operator on E. We express the multiplicities of the associated representati...