A NOTE ON THE CONTINUITY OF OPERATORS INTERTWINING WITH CONVOLUTION OPERATORS

A note on certain convolution operators

In this note we consider a certain class of convolution operators acting on the Lp spaces of the one dimensional torus. We prove that the identity minus such an operator is nicely invertible on the subspace of functions with mean zero. 2010 Mathematics Subject Classification. Primary 47G10; Secondary 47B34, 26D10.

Continuity of Generalized Intertwining Linear Operators for Operators with Property (δ) and Hyponormal Operators

In this paper, we show that for a hyponormal operator the analytic spectral subspace coincides with the algebraic spectral subspace. Using this result, we have the following result: Let T be a operator with property (δ) on a Banach space X and let S be a hyponormal operator on a Hilbert space H. Then every generalized intertwining linear operator θ : X → H for (S, T ) is continuous if and only ...

A Note on Calderón-zygmund Singular Integral Convolution Operators

Logarithmic Intertwining Operators and Vertex Operators

This is the first in a series of papers where we study logarithmic intertwining operators for various vertex subalgebras of Heisenberg vertex operator algebras. In this paper we examine logarithmic intertwining operators associated with rank one Heisenberg vertex operator algebra M(1)a, of central charge 1 − 12a . We classify these operators in terms of depth and provide explicit constructions ...

Continuityof Operators Intertwiningwith Convolution Operators

Let G be a locally compact abelian group, let m be a bounded complex-valued Borel measure on G; and let Tm be the corresponding convolution operator on LðGÞ: Let X be a Banach space and let S be a continuous linear operator on X : Then we show that every linear operator F : X ! LðGÞ such that FS 1⁄4 TmF is continuous if and only if the pair ðS;TmÞ has no critical eigenvalue. # 2002 Elsevier Sci...