compact operator

From: novis <standshik@xxxxxxxxx>
Date: Fri, 10 Aug 2007 00:14:05 -0700

dear all, can you please help me with this question? suppose A: X -->Y
is a compact operator form hilbert space X to hilbert space Y. and
B=adjoint(A): Y-->X. now will the spectrum of operator AB and operator
BA be same? i.e will operators AB and BA have same eigenvalues? thanks

.

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