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Since $T$ is a bounded symmetric positive operator, by the spectral mapping theorem$f( r)=\inf \sigma(T)$, a constant function. So the answer is: yes, if and only if $\inf \sigma(T)>0$, that is, $T$ is invertible.
Since $T$ is a bounded symmetric positive operator, by the spectral mapping theorem$f( r)=\inf \sigma(T)$, a constant function. So the answer is: yes, if and only if $\inf \sigma(T)>0$, that is, $T$ is invertible.
Since $T$ is a bounded symmetric positive operator $f( r)=\inf \sigma(T)$, a constant function. So the answer is: yes, if and only if $\inf \sigma(T)>0$, that is, $T$ is invertible.
Since $T$ is a bounded symmetric positive operator, by the spectral mapping theorem $f( r)=\inf \sigma(T)$, a constant function. So the answer is: yes, if and only if $\inf \sigma(T)>0$, that is, $T$ is invertible.
