Trace-Class and Nuclear Operators

Abstract

This paper explores the long journey from projective tensor products of a pair of Banach spaces, passing through the definition of nuclear operators still on the realm of projective tensor products, to the of notion of trace-class operators on a Hilbert space, and shows how and why these concepts (nuclear and trace-class operators, that is) agree in the end.

Keywords

• nuclear operators
• projective tensor product
• trace-class operators
• 47b10
• 47a80
• 46m05