A new look at some familiar spaces of intertwining operators

Ralph Allen Gellar and Lavon Barry Page

Vol. 47 (1973), No. 2, 435–441

DOI: 10.2140/pjm.1973.47.435

Abstract

When T₁ and T₂ are bounded operators on a Hilbert space, solutions to the equation XT₁ = T₂X are called intertwining operators for T₁ and T₂. Several familiar spaces of intertwining operators are examined and a new method is proposed for studying the duality relationship that frequently exists between the space of intertwining operators and its subspace of compact intertwining operators.

Mathematical Subject Classification 2000

Primary: 47B47

Milestones

Received: 1 March 1972

Revised: 26 February 1973

Published: 1 August 1973