Two sided ideals of operators

Two Sided Ideals of Operators

1. Let X be a Banach space, and B(X) the Banach algebra of all bounded linear operators in X. The closed two sided ideals of B(X) (actually, of any Banach algebra) form a complete lattice L(X). Aside from very concrete cases, L(X) has not yet been determined; for instance, when X = l, l ^ p < « > , L(X) is a chain (i.e., totally ordered) with three elements: {o}, B(X) and the ideal C(X) of comp...

On One-Sided Ideals of Rings of Linear Transformations

Local two-sided bounds for eigenvalues of self-adjoint operators

We examine the equivalence between an extension of the Lehmann-Maehly-Goerisch method developed a few years ago by Zimmermann and Mertins, and a geometrically motivated method developed more recently by Davies and Plum. We establish a general framework which allows sharpening various previously known results in these two settings and determine explicit convergence estimates for both methods. We...

ONE - SIDED k - IDEALS ANDh - IDEALS IN SEMIRINGSH

ideals of these kinds; congruence class semirings. Abstract: Since they are closer related to the ring-theoretical concept of ideals than arbitrary semiring ideals, two-sided k-ideals and h-ideals occur in several statements on semirings. In this paper we investigate those ideals and also left-sided ones in arbitrary semirings S with commutative addition. For instance, we prove (for the rst tim...

An Algebra Containing the Two-Sided Convolution Operators

We present an intrinsically defined algebra of operators containing the right and left invariant Calderón-Zygmund operators on a stratified group. The operators in our algebra are pseudolocal and bounded on Lp (1 < p <∞). This algebra provides an example of an algebra of singular integrals that falls outside of the classical Calderón-Zygmund theory.