Christoph Schmoeger
Abstract
Suppose that A and B are bounded linear operators on a Banach space such that AB is a Fredholm operator. In general, BA is not a Fredholm operator. In this note we show that BA is a generalised Fredholm operator in the sense of Caradus.
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Suppose that A and B are bounded linear operators on a Banach space such that AB is a Fredholm operator. In general, BA is not a Fredholm operator. In this note we show that BA is a generalised Fredholm operator in the sense of Caradus.
Key concepts: Fredholm theory, Fredholm operator, Bounded operator, Compact operator, Finite-rank operator, Mathematics, Operator (biology), Fredholm integral equation