Question

Let $H$ be a Hilbert space and $S, T \in B(H)$. Show that if $S T=T S$ then $\rho(S T) \leqslant \rho(S) \rho(T)$.

   Let $H$ be a Hilbert space and $S, T \in B(H)$. Show that if $S T=T S$ then $\rho(S T) \leqslant \rho(S) \rho(T)$.

Integral equations: a practical treatment, from spectral theory to applications

Integral equations: a practical treatment, from spectral theory to applications

David Porter, David… 1st Edition

Chapter 3, Problem 19

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Step 1: Recall that for any operator $A \in B(H)$, the spectral radius $\rho(A)$ is defined as the maximum modulus of the eigenvalues of $A$. Show more…

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Let $H$ be a Hilbert space and $S, T \in B(H)$. Show that if $S T=T S$ then $\rho(S T) \leqslant \rho(S) \rho(T)$.

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