MHB Is the Triangle Inequality Applicable to Norms of Integral Operators?

[sarrah1]

Can I always say without reservation that for any two integral operators $K$ and $L$ defined as follows say
$(Ky)(x)=\int_{a}^{b} \,k(x,s)y(s)ds$
that
$||L||+||K-L||\ge||K||$
thanks
Sarrah

 

[Opalg]

Can I always say without reservation that for any two integral operators $K$ and $L$ defined as follows say
$(Ky)(x)=\int_{a}^{b} \,k(x,s)y(s)ds$
that
$||L||+||K-L||\ge||K||$
thanks
Sarrah

That follows from the triangle inequality: $\|K\| = \|K-L+L\| \leqslant \|K-L\| + \|L\|.$